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: 49

Answer

$\frac{a^{30}}{b^{12}}$

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, $(a^{-5}b^{2})^{-6}=(a^{-5})^{-6}(b^{2})^{-6}=a^{-5\times-6}b^{2\times-6}=a^{30}b^{-12}=a^{30}\times\frac{1}{b^{12}}=\frac{a^{30}}{b^{12}}$.
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