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: 30

Answer

$\dfrac{1}{216}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{3^{}}{2^{-1}} \right)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3^{1(-3)}}{2^{-1(-3)}} \\\\= \dfrac{3^{-3}}{2^{3}} \\\\= \dfrac{1}{3^{3}\cdot2^{3}} \\\\= \dfrac{1}{27\cdot8} \\\\= \dfrac{1}{216} .\end{array}
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