# Chapter 11 - Additional Topics - 11.3 - Fractional Exponents - Problem Set 11.3 - Page 489: 79

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

#### 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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