1 Math Powers and Exponents. 2 What Are You Learning? I CAN write powers as a product of the same...

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Math

Powers and Exponents

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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.

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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

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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