Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises - Page 278: 142

Answer

$\dfrac{x^{20}}{64y^{14}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{8x^{-6}y^3}{x^4y^{-4}} \right)^{-2} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{8^{-2}x^{-6(-2)}y^{3(-2)}}{x^{4(-2)}y^{-4(-2)}} \\\\= \dfrac{8^{-2}x^{12}y^{-6}}{x^{-8}y^{8}} \\\\= 8^{-2}x^{12-(-8)}y^{-6-8} \\\\= 8^{-2}x^{12+8}y^{-6-8} \\\\= 8^{-2}x^{20}y^{-14} \\\\= \dfrac{x^{20}}{8^{2}y^{14}} \\\\= \dfrac{x^{20}}{64y^{14}} .\end{array}
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