Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set: 50

Answer

$\frac{16}{x^{10}}$

Work Step by Step

We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $(4^{-1}x^{5})^{-2}=(4^{-1})^{-2}(x^{5})^{-2}=4^{-1\times-2}x^{5\times-2}=4^{2}x^{-10}=16\times\frac{1}{x^{10}}=\frac{16}{x^{10}}$.
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