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: 43

Answer

$49a^{4}b^{10}c^{2}$

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, $(-7a^{2}b^{5}c)^{2}=(-7)^{2}\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}=49\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}$. 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, $49\times (a^{2})^{2}\times (b^{5})^{2}\times c^{2}=49\times a^{2\times2}\times b^{5\times2}\times c^{2}=49a^{4}b^{10}c^{2}$.
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