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 - Page 344: 41

Answer

$x^{10}y^{15}$

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, $(x^{2}y^{3})^{5}=(x^{2})^{5}\times (y^{3})^{5}$. 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, $(x^{2})^{5}\times (y^{3})^{5}=x^{2\times5}\times y^{3\times5}=x^{10}y^{15}$.
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