Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 1

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 2

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 3

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 4

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 5

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 6

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 7

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 8

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 9

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 10

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 11

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

eSolutions Manual - Powered by Cognero Page 12

Chapter Review

Write each expression using exponents.1. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

2. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

3. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

4. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

5. 35

SOLUTION:  

6. 2 • 43

SOLUTION:  

7. (–4)3

SOLUTION:  

8. 40 • 5

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

9. x2 – 6

SOLUTION:  

10. w3 + y

2

SOLUTION:  

11. 2(y + z3)

SOLUTION:  

12. w4x

2yz

SOLUTION:  

13. Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

14. Xander ran a total of 53 kilometers last month. How many kilometers did he run?

SOLUTION:  

So, Xander ran 125 kilometers.

Write each expression using a positive exponent.

15. 9–4

SOLUTION:  

9–4

=

16. (–10)–2

SOLUTION:  

(–10)–2

=

17. m–5

SOLUTION:  

m–5 =

18. c–5

SOLUTION:  

c–5 =

19. (–4)–3

SOLUTION:  

(–4)–3

=

20. y–9

SOLUTION:  

y–9

=

Write each fraction as an expression using a negative exponent other than –1.

21. 

SOLUTION:  

= 6–3

22. 

SOLUTION:  

or  or 

23. 

SOLUTION:  

24. 

SOLUTION:  

25. 

SOLUTION:  

or

26. 

SOLUTION:  

27. One millimeter equals 0.001 meter. Write the decimal using a negative exponent.

SOLUTION:  

Find each product or quotient. Express using exponents.

28. 35 • 3–2

SOLUTION:  

29. (–7) • (–7)4

SOLUTION:  

30. m3 • m6

SOLUTION:  

31. x8 • x

SOLUTION:  

32. (2h7)(6h)

SOLUTION:  

33. (5a–3

)(–6a4)

SOLUTION:  

34. 

SOLUTION:  

35. 

SOLUTION:  

36. Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how many times

farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the distance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Express each number in standard form.

37. 5.82 × 103

SOLUTION:  

38. 9.0 × 10–2

SOLUTION:  

39. 1.1 × 10–4

SOLUTION:  

40. 2.25 × 105

SOLUTION:  

Express each number in scientific notation.41. 379

SOLUTION:  

42. 0.000561

SOLUTION:  

43. 47,000

SOLUTION:  

44. 0.0072

SOLUTION:  

45. The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Evaluate each expression. Express the result in scientific notation.

46. (4.45 × 109)(1.3 × 106)

SOLUTION:  

47. 

SOLUTION:  

48. (7.4 × 104) + (3.56 × 10

5)

SOLUTION:  

49. (3.6 × 107) – (2.85 × 105

)

SOLUTION:  

50. A fin whale weighs 9.92 × 104 pounds. A blue whale weighs 2.87 × 10

5 pounds. Estimate how many more pounds

the blue whale weighs than the fin whale.

SOLUTION:  

The blue whale weighs about 2 × 105

pounds more than the fin whale.

51. A male elephant weighs 1.5 × 104 pounds. A female elephant weighs 7.9 × 10

3 pounds. How much more does the

male elephant weigh than the female elephant? Express your result in scientific notation.

SOLUTION:  

The male elephant weights 7.1 × 103

pounds more than the female elephant.

Find each square root or cube root.

52. 

SOLUTION:  

= 13

53. 

SOLUTION:  

= –5

54. 

SOLUTION:  

= –4

55. 

SOLUTION:  

= 9

Estimate each square root or cube root to the nearest integer.

56. 

SOLUTION:  

The first perfect square less than 15 is 9.  = 3

The first perfect square greater than 15 is 16.  = 4

The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9,  is closer to 4 than to 3.

57. 

SOLUTION:  

The first perfect square less than 52 is 49.  = 7

The first perfect square greater than 52 is 64.  = 8

The negative square root of 52 is between the integers –7 and –8. Since 54 is closer to 49 than to 64,  is closerto –7 than to –8.

58. 

SOLUTION:  

The first perfect cube less than 90 is 64.  = 4

The first perfect cube greater than 90 is 125.  = 5

The cube root of 90 is between the integers 4 and 5. Since 90 is closer to 64 than to 125,  is closer to 4 than to 5.

59. 

SOLUTION:  

The first perfect cube less than 415 is 343.  = 7

The first perfect cube greater than 415 is 512.  = 8

The cube root of 415 is between the integers 7 and 8. Since 415 is closer to 343 than to 512,  is closer to 7 than to 8.

60. The period of a pendulum is the time it takes to make one complete swing. The period P of a pendulum is given by

the formula   , where ℓ is the length of the pendulum. If a clock’s pendulum is 8 feet long, find the

period.

SOLUTION:  To find the period, substitute 8 for ℓ.

The period of the pendulum is 3.14 seconds.

Name all of the sets of numbers to which each real number belongs. Write natural, whole, integer, rational, or irrational.

61. 18

SOLUTION:  

Since 18 = , this number is a rational number. So, 18 is a natural number, whole number, an integer, and a rational

number.

62. 

SOLUTION:  

is written as a fraction, so it is a rational number.

63. 

SOLUTION:  

cannot be written as a fraction, so it is an irrational number.

64. 

SOLUTION:  

Since , this number is a rational number.

Replace the  Ο  with <, >, or = to make a true statement.

65.    Ο     

SOLUTION:  

= 6.2525…

 = 6.2449…

Since  is to the right of  ,  >  .

66.    Ο  

SOLUTION:  

= –8.3666…

−8 = –8.2

Since  is to the left of −8 ,  < −8 .

67.     Ο  

SOLUTION:  

−11   = –11.1111…

 = –11.1355…

Since −11 is to the right of , −11 > .

68.    Ο    

SOLUTION:  

= 8.2462…

 = 8.4444…

Since  is to the left of  ,  <  .

Solve each equation. Round to the nearest tenth, if necessary.

69. m3

= 512

SOLUTION:  

The solutions is 8.

70. 4y2 = 5.76

SOLUTION:  

The solutions are 1.2 and –1.2.

71. The formula A ≈ 3.14r2 can be used to determine the area of a circle, where A is the area and r is the distance from

the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth.

SOLUTION:  To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle.

Substitute 700 for A in the equation A ≈ 3.14r2.

Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet.

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