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: 11

Answer

$-\dfrac{27}{8}$

Work Step by Step

Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$ and the laws of exponents, the given expression, $ \left( -\dfrac{2}{3} \right)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{-2}{3} \right)^{-3} \\\\= \dfrac{(-2)^{-3}}{3^{-3}} \\\\= \dfrac{3^{3}}{(-2)^{3}} \\\\= \dfrac{27}{-8} \\\\= -\dfrac{27}{8} .\end{array}
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