1 math powers and exponents. 2 what are you learning? i can write powers as a product of the same...
TRANSCRIPT
1
Math
Powers and Exponents
2
What Are You Learning?
• I CAN write powers as a product of the same factor.
• I CAN write products in exponential form.
• I CAN evaluate exponents.
3
Why Do You Need To Know This?
Exponents are used in the real-world to represent extremely large and small numbers. They are also used in solving problems.
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Vocabulary Words
Factors—Two or more numbers multiplied together to form a product.
Example—2 • 3 = 6 The numbers 2 and 3 are factors.
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Vocabulary
Base—The common factor or number being multiplied.
5 • 5 • 5 • 5 • 5
Five is the base
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Vocabulary
Exponent—Number that tells how many times the base is used as a factor.
4²--2 is the exponent and it shows that 4 will be multiplied two times. 4 • 4
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Name the exponent and base.
A. 75
B. (-10)²
C. -22
D. 8³
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Vocabulary
Powers—Numbers expressed using exponents.
4² and 6³ are examples of powers.
4² is read “four to the second power.” 6³ is read “six to the third power.”
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Write each power in words
a. 12¹
b. 5²
c. 6³
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Vocabulary
Squared—A number multiplied by itself two times.
4 x 4 or 4² The four is being squared.
Cubed—A number multiplied by itself three times.
2 x 2 x 2 or 2³
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Write Numbers in Exponential Form
Exponential Form—Numbers written with exponents.
Example 1—Write 3 · 3 · 3 in exponential form.
3 is the base. It is used as a factor 3 times. So, the exponent is 3.
3 · 3 · 3 = 3³
12
Write each expression using exponents.
A. 5 · 5 · 5
B. 12 · 12 · 12 · 12 · 12
C. 9 · 9 · 9 · 9 · 9 · 9
D. a · b · b · a · a · b
E. (-3)(-3)(-3)(-3)
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Write each expression using exponents.
A. r · r · r · r · s · s
B. -2 · y · x · y
C. (-2) · (-2) · t · t · t · t
D. x · x · y · y · z
E. 5 · 5 · 4 · 2 · 5 · 4
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Write the product 8 • 8 • 8 in exponential form.
38 8
• 3 83 51
2
3% 0%
90%
6%
1. 38
2. 8 • 3
3. 83
4. 512
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33
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Write Powers as Products
Example 1—75
The base is 7. The exponent 5 means that 7 is used as a factor 5 times. 75 = 7 · 7 · 7 · 7 · 7
Example 2—3²
The base is 3. The exponent 2 means the 3 is used as a factor two times. 3² = 3 · 3
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Your Turn
Write each power as a product of the same factor.
a. 83
b. 4 to the sixth power
c. 2³ · 3² · 7
d. 3 to the third power · 4 squared
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Write the power 73 as a product of the same factor.
3 •
3 • 3
• 3
...
7 •
7 • 7
7 •
334
3
10%0%0%
90%1. 3 • 3 • 3 • 3 • 3 • 3 • 3
2. 7 • 7 • 7
3. 7 • 3
4. 343
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33
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Vocabulary
Evaluate—Find the value of an expression.
Standard Form—Numbers written without exponents.
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Write Powers in Standard Form
Evaluate each expression.
Example 1—25 = 2 · 2 · 2 · 2 · 2 = 32
Example 2—4³ = 4 · 4 · 4 = 64
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Evaluate each expression
a. 10²
b. 7 to the third power
c. 54
d. 8³
e. 6 to the fourth power
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Evaluate 24
2 •
2 • 2
• 2 8 32 16
23%
58%
3%
16%
1. 2 • 2 • 2 • 2
2. 8
3. 32
4. 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33
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Evaluate each expression
a. 21 · 3²
b. 7² · 3³
c. 3 · 2² · 4³
d. 7 · 6³ · 10³
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Class Work
Pg. 12 17-35 ODD ONLY