Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set: 29

Answer

$\dfrac{32}{x^{5}}$

Work Step by Step

Using $\left( \dfrac{a}{b} \right)^{x}=\dfrac{a^x}{b^x} $, the given expression, $ \left( \dfrac{x}{2} \right)^{-5} $, is equivalent to \begin{array}{l} \dfrac{x^{-5}}{2^{-5}} .\end{array} Using $a^{-x}=\dfrac{1}{a^{x}}$ and $\dfrac{1}{a^{-x}}=a^x$, the expression above is equivalent to \begin{array}{l} \dfrac{2^{5}}{x^{5}} \\\\= \dfrac{32}{x^{5}} .\end{array}
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