Five-Minute Check (over Lesson 1–2)

Main Idea and Vocabulary

Example 1:Write Powers and Products

Example 2:Write Powers and Products

Example 3:Use Powers to Solve a Problem

Example 4:Prime Factorization Using Exponents

Example 5:Prime Factorization Using Exponents

Example 6:Prime Factorization Using Exponents

• base

• exponent

• power

• squared

• cubed

• Use powers and exponents in expressions.

Write Powers and Products

Write 5 × 5 × 5 × 5 using an exponent.

The base is 5. Since 5 is used as a factor four times, the exponent is 4.

5 × 5 × 5 × 5 = 54 Write as a power.

Answer: 54

1. A

2. B

3. C

4. D0% 0%0%0%

A. 414

B. 47

C. 74

D. 142

Write 4 × 4 × 4 × 4 × 4 × 4 × 4 using an exponent.

Write Powers and Products

Write 83 as a product of the same factor. Then find the value.

The base is 8. The exponent is 3. So, 8 is used as a factor three times.

83 = 8 × 8 × 8 Write 83 as a product.

= 512 Multiply.

Answer: 8 × 8 × 8; 512

1. A

2. B

3. C

4. D

0% 0%0%0%

A. 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2; 256

B. 6 × 6 × 6 × 6; 1,296

C. 4 × 4 × 4 × 4 × 4 × 4; 4,096

D. 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3; 6,561

Write 64 as a product of the same factor. Then find the value.

The distance from Boston to Chicago is about 103 miles. What is this number?

103 = 10 × 10 × 10 Write 103 as a product.

= 1,000 Multiply.

Answer: So, the distance from Boston to Chicago is about 1,000 miles.

Use Powers to Solve a Problem

1. A

2. B

3. C

4. D0% 0%0%0%

A. 12 ft

B. 24 ft

C. 36 ft

D. 64 ft

SWIMMING POOL The length of a new swimming pool being built at the community recreation center is listed as 26 feet. What is the length of the new pool?

Write the prime factorization of 108 using exponents.

108 = 2 × 2 × 3 × 3 × 3 Write the prime factorization.

Answer: 22 × 33

Prime Factorization Using Exponents

= 22 × 33 Write products of identical factors using exponents.

1. A

2. B

3. C

4. D0% 0%0%0%

A. 24 × 32

B. 22 × 34

C. 22 × 62

D. 32 × 42

Write the prime factorization of 144 using exponents.

Write the prime factorization of 80 using exponents.

80= 2 × 2 × 2 × 2 × 5Write the prime factorization.

Answer: 24 × 5

Prime Factorization Using Exponents

= 24 × 5 Write products of identical factors using exponents.

1. A

2. B

3. C

4. D0% 0%0%0%

A. 22 × 32

B. 24 × 3

C. 2 × 34

D. 33 × 6

Write the prime factorization of 162 using exponents.

Write the prime factorization of 450 using exponents.

450 = 2 × 3 × 3 × 5 × 5 Write the prime factorization.

Answer: 2 × 32 × 52

Prime Factorization Using Exponents

= 2 × 32 × 52Write products of identical factors using exponents.

1. A

2. B

3. C

4. D0% 0%0%0%

A. 23 × 3 × 5

B. 22 × 32 × 5

C. 32 × 4 × 5

D. 2 × 32 × 6

Write the prime factorization of 180 using exponents.

End of the Lesson

Five-Minute Check (over Lesson 1–2)

Image Bank

Math Tools

Rectangular Arrays

Area of Rectangles and Squares

1. A

2. B

3. C0% 0%0%

A. prime

B. composite

C. neither

Tell whether 23 is prime, composite, or neither.

(over Lesson 1-2)

1. A

2. B

3. C0% 0%0%

A. prime

B. composite

C. neither

Tell whether 57 is prime, composite, or neither.

(over Lesson 1-2)

1. A

2. B

3. C

4. D0% 0%0%0%

A. 2 × 30

B. 4 × 15

C. 4 × 3 × 5

D. 2 × 2 × 3 × 5

Find the prime factorization of 60.

(over Lesson 1-2)

1. A

2. B

3. C

4. D0% 0%0%0%

A. 4 × 21

B. 2 × 6 × 7

C. 2 × 2 × 3 × 7

D. 6 × 14

Find the prime factorization of 84.

(over Lesson 1-2)

1. A

2. B

3. C

4. D0% 0%0%0%

A. 25, 50, 75, 100

B. 25, 50, 75

C. 50, 100

D. 5, 25

Which numbers less than 110 contain 5 × 5 in their prime factorizations?

(over Lesson 1-2)

1. A

2. B

3. C

4. D0% 0%0%0%

A. 23 × 33 × 5

B. 22 × 32 × 52

C. 22 × 33 × 5

D. 2 × 33 × 52

Which is the prime factorization of 540?

(over Lesson 1-2)