## Elementary Algebra

Published by Cengage Learning

# Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 223: 18

#### Answer

$\dfrac{81}{16}$

#### 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, $\dfrac{1}{\left( \dfrac{3}{2} \right)^{-4}} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{3}{2} \right)^{4} \\\\= \dfrac{3^4}{2^4} \\\\= \dfrac{81}{16} .\end{array}

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