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 - Practice: 11

Answer

$\frac{a^{20}}{b^{35}}$

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, $(a^{-4}b^{7})^{-5}=(a^{-4})^{-5}(b^{7})^{-5}=a^{-4\times-5}b^{7\times-5}=a^{20}b^{-35}=a^{20}\times\frac{1}{b^{35}}=\frac{a^{20}}{b^{35}}$.
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