Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6: 81

Answer

$\dfrac{1}{8x^3}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{2x^{-1}}{x^{-2}} \right)^{-3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2^{-3}x^{-1(-3)}}{x^{-2(-3)}} \\\\= \dfrac{2^{-3}x^{3}}{x^{6}} \\\\= 2^{-3}x^{3-6} \\\\= 2^{-3}x^{-3} \\\\= \dfrac{1}{2^{3}x^3} \\\\= \dfrac{1}{8x^3} .\end{array}
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