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: 51



Work Step by Step

We are given that the square has sides of length $8z^{5}$ decimeters. We know that the area of a square is calculated as $area=length^{2}$. 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, $area=(8z^{5})^{2}=8^{2}(z^{5})^{2}=64(z^{5})^{2}$. 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, $area=64(z^{5})^{2}=64z^{5\times2}=64z^{10}$.
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