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More Multiplication Properties of Exponents

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. 3 2 • 3 2 • 3 2 2. 2 3 • 2 3 • 2 3 • 2 3 3. 5 7 • 5 7 • 5 7 • 5 7 4. 7 • 7 • 7 Simplify. 5. x 3 • x 3 6. a 2 • a 2 • a 2

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More Multiplication Properties of Exponents

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  1. 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 • 322. 23 • 23 • 23 • 23 3. 57 • 57 • 57 • 574. 7 • 7 • 7 Simplify. 5.x3 • x36.a2 • a2 • a2 7.y–2 • y–2 • y–28.n–3 • n–3 4-4

  2. More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-4 Solutions 1. 32 • 32 • 32 = 3(2 + 2 + 2) = 36 2. 23 • 23 • 23 • 23 = 2(3 + 3 + 3 + 3) = 212 3. 57 • 57 • 57 • 57 = 5(7 + 7 + 7 + 7) = 528 4. 7 • 7 • 7 = 73 5.x3 • x3 = x(3 + 3) = x6 6.a2 • a2 • a2 = a(2 + 2 + 2) = 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

  3. Multiply exponents when raising a power to a power. (a3)4 = a3• 4 Simplify. = a12 More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-4 Simplify (a3)4. 4-4

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

  5. (4x3)2 = 42(x3)2 Raise each factor to the second power. Multiply exponents of a power raised to a power. = 42x6 = 16x6 Simplify. More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-4 Simplify (4x3)2. 4-4

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

  7. Raise each factor within parentheses to the second power. 102 • (3 108)2 = 102 • 32 • (108)2 = 102 • 32 • 1016 Simplify (108)2. Use the Commutative Property of Multiplication. = 32 • 102 • 1016 Add exponents of powers with the same base. = 32 • 102 + 16 Simplify. Write in scientific notation. = 9  1018 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. 4-4

  8. x16 y6 More Multiplication Properties of Exponents ALGEBRA 1 LESSON 8-4 Simplify each expression. 1. (x4)52.x(x5y–2)3 3. (5x4)34. (1.5  105)2 5. (2w–2)4(3w2b–2)36. (3  10–5)(4  104)2 x20 2.25  1010 125x12 432b6w2 4.8  103 4-4

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