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: 38

Answer

$\frac{1}{x^{2}}$

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, $\frac{(x^{2})^{5}}{(x^{4})^{3}}=\frac{x^{2\times5}}{x^{4\times3}}=\frac{x^{10}}{x^{12}}=x^{10-12}=x^{-2}=\frac{1}{x^{2}}$.
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