Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3: 79

Answer

$\frac{125x^\frac{3}{2}}{216y}$

Work Step by Step

Since the expression within the parenthesis cannot be reduced through common factors, the only way to simplify the expression is to raise each term in the expression to the power of 3: $(\frac{5x^\frac{1}{2}}{6y^\frac{1}{3}})^{3}$ =$\frac{5^{3}\times (x^\frac{1}{2})^{3}}{6^{3}\times (y^\frac{1}{3})^{3}}$ =$\frac{125\times (x^\frac{3}{2})}{216\times (y^\frac{3}{3})}$ =$\frac{125\times (x^\frac{3}{2})}{216\times (y)}$ =$\frac{125x^\frac{3}{2}}{216y}$
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