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: 30

Answer

$\dfrac{16}{a^{4}}$

Work Step by Step

Using $\left( \dfrac{a}{b} \right)^{x}=\dfrac{a^x}{b^x} $, the given expression, $ \left( \dfrac{a}{2} \right)^{-4} $, is equivalent to \begin{array}{l} \dfrac{a^{-4}}{2^{-4}} .\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^{4}}{a^{4}} \\\\= \dfrac{16}{a^{4}} .\end{array}
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