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Lesson Menu 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

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Main Idea/Vocabulary base exponent power squared cubed Use powers and exponents in expressions.

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Example 1 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 = 5 4 Write as a power. Answer: 5 4

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1.A 2.B 3.C 4.D Example 1 A.4 14 B. 4 7 C. 7 4 D. 14 2 Write 4 × 4 × 4 × 4 × 4 × 4 × 4 using an exponent.

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Example 2 Write Powers and Products Write 8 3 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. 8 3 = 8 × 8 × 8Write 8 3 as a product. = 512Multiply. Answer: 8 × 8 × 8; 512

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1.A 2.B 3.C 4.D Example 2 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 6 4 as a product of the same factor. Then find the value.

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Example 3 The distance from Boston to Chicago is about 10 3 miles. What is this number? 10 3 = 10 × 10 × 10Write 10 3 as a product. = 1,000Multiply. Answer: So, the distance from Boston to Chicago is about 1,000 miles. Use Powers to Solve a Problem

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1.A 2.B 3.C 4.D Example 3 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 2 6 feet. What is the length of the new pool?

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Example 4 Write the prime factorization of 108 using exponents. 108= 2 × 2 × 3 × 3 × 3 Write the prime factorization. Answer: 2 2 × 3 3 Prime Factorization Using Exponents = 2 2 × 3 3 Write products of identical factors using exponents.

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1.A 2.B 3.C 4.D Example 4 A.2 4 × 3 2 B.2 2 × 3 4 C.2 2 × 6 2 D.3 2 × 4 2 Write the prime factorization of 144 using exponents.

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Example 5 Write the prime factorization of 80 using exponents. 80= 2 × 2 × 2 × 2 × 5Write the prime factorization. Answer: 2 4 × 5 Prime Factorization Using Exponents = 2 4 × 5Write products of identical factors using exponents.

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1.A 2.B 3.C 4.D Example 5 A.2 2 × 3 2 B.2 4 × 3 C.2 × 3 4 D.3 3 × 6 Write the prime factorization of 162 using exponents.

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Example 6 Write the prime factorization of 450 using exponents. 450= 2 × 3 × 3 × 5 × 5Write the prime factorization. Answer: 2 × 3 2 × 5 2 Prime Factorization Using Exponents = 2 × 3 2 × 5 2 Write products of identical factors using exponents.

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1.A 2.B 3.C 4.D Example 6 A.2 3 × 3 × 5 B.2 2 × 3 2 × 5 C.3 2 × 4 × 5 D.2 × 3 2 × 6 Write the prime factorization of 180 using exponents.

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End of the Lesson

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Resources Five-Minute Check (over Lesson 1–2) Image Bank Math Tools Rectangular Arrays Area of Rectangles and Squares

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1.A 2.B 3.C Five Minute Check 1 A.prime B.composite C.neither Tell whether 23 is prime, composite, or neither. (over Lesson 1-2)

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1.A 2.B 3.C Five Minute Check 2 A.prime B.composite C.neither Tell whether 57 is prime, composite, or neither. (over Lesson 1-2)

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1.A 2.B 3.C 4.D Five Minute Check 3 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)

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1.A 2.B 3.C 4.D Five Minute Check 4 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)

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1.A 2.B 3.C 4.D Five Minute Check 5 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)

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1.A 2.B 3.C 4.D Five Minute Check 6 A.2 3 × 3 3 × 5 B.2 2 × 3 2 × 5 2 C.2 2 × 3 3 × 5 D.2 × 3 3 × 5 2 Which is the prime factorization of 540? (over Lesson 1-2)

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