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: 42

Answer

$-\frac{1}{a}$

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, $\frac{15a^{4}}{-15a^{5}}=\frac{15}{-15}\times a^{4-5}=-1\times a^{-1}=-1\times\frac{1}{a}=-\frac{1}{a}$.
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