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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 (For help, go to Lesson 8-3.) Rewrite each expression using each base only once. 1. 32 • 32 • • 23 • 23 • 23 3. 57 • 57 • 57 • • 7 • 7 Simplify. 5. x3 • x3 6. a2 • a2 • a2 7. y–2 • y–2 • y–2 8. n–3 • n–3 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Solutions • 32 • 32 = 3( ) = 36 • 23 • 23 • 23 = 2( ) = 212 • 57 • 57 • 57 = 5( ) = 528 4. 7 • 7 • 7 = 73 5. x3 • x3 = x(3 + 3) = x6 6. a2 • a2 • a2 = a( ) = a6 7. y–2 • y–2 • y–2 = y(–2 + (–2) + (–2)) = y–6 = 8. n–3 • n–3 = n(–3 + (–3)) = n–6 = 1 y 6 1 n 6 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Simplify (a3)4. Multiply exponents when raising a power to a power. (a3)4 = a3 • 4 Simplify. = a12 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Simplify b2(b3)–2. b2(b3)–2 = b2 • b3 • (–2) Multiply exponents in (b3)–2. = b2 • b–6 Simplify. = b2 + (–6) Add exponents when multiplying powers of the same base. Simplify. = b–4 1 b4 = Write using only positive exponents. 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Simplify (4x3)2. (4x3)2 = 42(x3)2 Raise each factor to the second power. = 42x6 Multiply exponents of a power raised to a power. = 16x6 Simplify. 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Simplify (4xy3)2(x3)–3. (4xy3)2(x3)–3 = 42x2(y3)2 • (x3)–3 Raise the three factors to the second power. = 42 • x2 • y6 • x–9 Multiply exponents of a power raised to a power. = 42 • x2 • x–9 • y6 Use the Commutative Property of Multiplication. = 42 • x–7 • y6 Add exponents of powers with the same base. 16y6 x7 = Simplify. 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 An object has a mass of 102 kg. The expression 102 • (3 108)2 describes the amount of resting energy in joules the object contains. Simplify the expression. 102 • (3 108)2 = 102 • 32 • (108)2 Raise each factor within parentheses to the second power. = 102 • 32 • 1016 Simplify (108)2. = 32 • 102 • 1016 Use the Commutative Property of Multiplication. = 32 • Add exponents of powers with the same base. = 9 1018 Simplify. Write in scientific notation. 4-4

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**More Multiplication Properties of Exponents**

ALGEBRA 1 LESSON 8-4 Simplify each expression. 1. (x4)5 2. x(x5y–2)3 3. (5x4)3 4. (1.5 105)2 5. (2w–2)4(3w2b–2)3 6. (3 10–5)(4 104)2 x16 y6 x20 2.25 1010 125x12 432 b6w2 4.8 103 4-4

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