copyright©amberpasillas2010 an exponent tells how many times a number is multiplied by itself. 8 3...

copyright©amberpasillas2010

An exponent tells how many times a number is multiplied by itself.

83Base

Exponent

#1

Factored Form

3 • 3 • a • a • a

Exponential Form

32a

3

x • y • x • 2 2x

2y

1

8•8•8 = 512

22 3

2 23 3 4

9


# 2When simplifying exponents you must watch the sign and the parenthesis!

52

= 5•5 = 25

–52

= –5•5 = –25

(-5)2

=(-5)(-5) = 25 –(5)2

= - (5)(5) = –251



Evaluate The Power#3

1)

2)

3)

4)

25

42

310

212

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

To find 5 on my calculator I type in

4

5 4^ = 625

5 yx 4 = 625

Try to find 9 = 7293



Powers of Ten

210

10

10

10

10

3

4

5

100

1,00010,000

100,000

10110

110

-1 = 0.1

# 4

10-2

1

110 2

1100

= 0.01

10-3 1

10 3 11000

= 0.001


Negative Exponents

# 5

EXAMPLES:

232

1

3

4( 5) 4

1

( 5)

For any integer n, a-n is the reciprocal of an

1nn

aa

A negative exponent is an inverse!


Any number to the zero power is ALWAYS ONE.

x0 = 1

Ex:

# 6

04 12 25 5 2 25 05 1

03 4 1 1


Exponents and Parenthesis

#7Factored Form

8 • x • x • xExponential Form

8x3

4(xy)(xy) 4(xy)2

(8x)3 (8x)(8x)(8x) = 8

3x

3

= 4 x2y

2

(5x3)

2 (5 x x x)(5 x x x) = 25x6

(2y2z)

2 (2 y y z) (2 y y z) = 22y

4z

2

= 512x3

= 52(x

3)2

= 4y4z

2


Fractions With Exponents

311) 2

222) 3

214) 3

225) 5

26) 9

12 2 2

2 23 3

231

9

252

254

219

181

18

49

# 8

213) 5

1 15 5 1

25


Negative Exponent Examples51) n

3 42) a b

44) 3a

45) 3a

26) 5x 3 03) m n

51n

3 41=

a b

413a

43a

41

3a 4

181a

215x

25

x

31 1

m

# 9

31

m


21

8

Just flip the fraction over to make the exponent positive!

28

1

2

2

8

1

#10

64

24

7

27

4

2

2

7

4 49

16

31

4

34

1

3

3

4

( 1)

64

1

64


When multiplying powers with the

same base, just ADD the exponents.

For all positive integers m and n:am • an = am + n

Ex :

#11

(32)(3

3) = (3 • 3) • (3 • 3 •3)

= 32+3 = 3

5

(x5)(x

4) = x

5+4 = x9


To find the power of a power, you MULTIPLY the

exponents . This is used when an exponentis on the outside of parenthesis.

# 12

= 53a

2•3b

3 (51a

2b)

3

(21x

3)5

= 25x

3•5

8(31y

8z)

2 = 8 (3

2y

8•2z

2)

= 125a6b

3

= 32x15

= 72y16

z2


#13

= x8+5

x8• x

5

(4a7b)

3 = 43a

7•3b

3

= x13

= 64a21

b3

Product of a Power Property

Power of a Power Property

= (-12)2(-3 • 4)

2

=144

Power of a Product Property

= (-12)(-12)


Prime Factorization is when you write a

number as the product of prime numbers. Factor Tree 36

#14

36 2 2 3 3 2 236 2 3

2 18

2 9

3 3

Circle the

prime numbers


Factoring#15

1)410m

15m=

2 5 m m m m 3 5 m =

32m

3

2)3

2

27a b

36ab=

3•3•3• • • •a a a b2• 2 •3•3• • •a b b =

23

4

a

b

12

2 6

2 3

2 2 3


# 16When Dividing Powers with the same base,

just SUBTRACT THE EXPONENTS. This is called the

Quotient of Powers Property.

x 5

x 2 =x x x x x

x x = x x x 3x

x5

x 2 =5 2x 3x

or


#17

2 315x y12xy

1512

2 1x 3 1y

54x 2y

2 315x y

12xy

3

3

5

4

21

25xy

4


COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same

3 52x 4x 8 3 5 x 8 8x

# 18

2(7ab)(2a )

14

1) 2) 2 3 4(2x y )( 3x y)

63a b 6x 4y


# 19 Dividing Powers With Negatives

Quotient of Powers Propertyx a

x b =a bx

3

4

6x

8x =

=3

4

6x

8x

3

4

3x

4x =3 43x x

4

=

73x

4

3

4

3x

4x =3 43

x4

=

73x

4


3 42x 5x

2 5 3 4x 710x

#20

Simplify.5 71) (8a ) (3a )

72) (-3a) (4a )

2 3 53) (9x y )(-2xy )

2 3 54) (6a bc )(5ab )

24 12a

12 8a

18 3x 8y

30 3a 6b 3c

1

1

11


# 21 Quotient of Powers Property

Quotient of Powers Propertyx a

x b =a bx

2

377

2 37 57 5

17

2 37 7

32

1 77

2 31 17 7

5

17

Same


Extras


Exponents & PowersAn exponent or power tells how manytimes a number is multiplied by itself.

34

BaseExponent

#1

25 “Five to the 2nd power” 5 5“Five squared”

37 “Seven to the 3rd power” 7 7 7 “Seven cubed”


Multiplying Powers: If bases are the same add exponents.

7 4 x x 7 4x 11xPower of a Power: Used when exponents are on the outside of parenthesis, just multiply exponents.

2 4 3(2a b )43 3 322 a b 6 128a b

Coefficients: The number in front of the variable is the coefficient. Multiply coefficients.

3 52x 4x 88x

#


Dividing Powers: If bases are the same subtract exponents.

15

126 6

15 126 36

Negative Exponent: To get rid of a negative exponent flip it over!

4 2 412

116

Zero Exponent: Anything to the zero power is always one!

0 329 1

#

copyright©amberpasillas2010 an exponent tells how many times a number is multiplied by itself. 8 3...

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