Explanation Rule used: Product Rule for Exponents: “If a is a real number, and m and n are natural numbers, then a m ⋅ a n = a m + n ”. Power Rule for Exponents: “If a is a real number, and m and n are natural numbers, then ( a m ) n = a m . n ”. Product to a Power Rule for Exponents: “If a , b are real numbers and n is a natural number, then ( a ⋅ b ) n = a n ⋅ b n ”. Calculation: The given expression is − 2 ( − 4 a 3 b 2 ) 2 ( 3 2 a b 5 ) 3 . Simplify the expression as follows. − 2 ( − 4 a 3 b 2 ) 2 ( 3 2 a b 5 ) 3 = − 2 ⋅ ( − 4 ) 2 ⋅ ( a 3 ) 2 ⋅ ( b 2 ) 2 ⋅ ( 3 2 ) 3 ⋅ a 3 ⋅ ( b 5 ) 3 [ ∵ ( a ⋅ b ) n = a n ⋅ b n ] = − 2 ⋅ 16 ⋅ a 3 ⋅ 2 ⋅ b 2 ⋅ 2 ⋅ 27 8 ⋅ a 3 ⋅ b 5 ⋅ 3 [ ∵ ( a m ) n = a m

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ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter 5.2, Problem 94E

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To simplify: The expression −2(−4a3b2)2(32ab5)3.

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Chapter 5.2, Problem 93E

Chapter 5.2, Problem 95E

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The expression − 2 ( − 4 a 3 b 2 ) 2 ( 3 2 a b 5 ) 3 .

Solution Summary: The author explains how to simplify the expression -2(-4a3b2) and Power Rule for Exponents.

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To simplify: The expression −2(−4a3b2)2(32ab5)3.

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