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: 37

Answer

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

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, $\frac{(a^{5})^{2}}{(a^{3})^{4}}=\frac{a^{5\times2}}{a^{3\times4}}=\frac{a^{10}}{a^{12}}=a^{10-12}=a^{-2}=\frac{1}{a^{2}}$.
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