Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 90

Answer

$\frac{64a^{24}}{b^{30}}$

Work Step by Step

According to the power rule for exponents, $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are integers and $a$ is a real number). Therefore, $(\frac{-2a^{4}}{b^{5}})^{6}=(\frac{-1\times2\times a^{4}}{b^{5}})^{6}=\frac{(-1)^{1\times6}2^{1\times6}a^{4\times6}}{b^{5\times6}}=\frac{(-1)^{6}\times2^{6}\times a^{24}}{b^{30}}=\frac{1\times64\times a^{24}}{b^{30}}=\frac{64a^{24}}{b^{30}}$.
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