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:
$(\frac{5x^\frac{1}{2}}{6y^\frac{1}{3}})^{3}$
=$\frac{5^{3}\times (x^\frac{1}{2})^{3}}{6^{3}\times (y^\frac{1}{3})^{3}}$
=$\frac{125\times (x^\frac{3}{2})}{216\times (y^\frac{3}{3})}$
=$\frac{125\times (x^\frac{3}{2})}{216\times (y)}$
=$\frac{125x^\frac{3}{2}}{216y}$
