Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.1 - Exponents - Exercise Set: 132

Answer

$16a^{16b}$

Work Step by Step

Based on the power of a product rule, we know that $(ab)^{n}=a^{n}b^{n}$ (where $n$ is a positive integer and $a$ and $b$ are real numbers). Therefore, $(2a^{4b})^{4}=2^{4}\times (a^{4b})^{4}=16\times (a^{4b})^{4}$. Based on the power rule for exponents, we know that $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are positive integers and $a$ is a real number). Therefore, $16\times (a^{4b})^{4}=16\times a^{4b\times4}=16a^{16b}$.
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