Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 15

Answer

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

Work Step by Step

We are given the expression $(\frac{a^{-4}}{a^{-5}})^{-2}$. First, we can use the power rule to simplify. $(\frac{a^{-4}}{a^{-5}})^{-2}=\frac{a^{-4\times-2}}{a^{-5\times-2}}=\frac{a^{8}}{a^{10}}$ Next, we can use the quotient rule. $a^{8-10}=a^{-2}=\frac{1}{a^{2}}$
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