Worked Solution #1 of 5, increasing in difficulty.

Expand the following:

\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large \sqrt{ x^{3} \ y^{2} } \\ \\ &\cssId{Step1}{\Large = \quad \left ( \ x^{3} \ y^{2} \right )^{ \frac {1}{2} } }\\ \\ &\cssId{Step2}{\Large = \quad x \ ^{\frac {3}{2}} \ y \ ^{\frac {2}{2}} }\\ \\ &\cssId{Step3}{\Large = \quad x \ ^{\frac {3}{2}} \ y \ ^{1} }\\ \\ &\cssId{Step4}{\Large = \quad x \ ^{\frac {3}{2}} \ y }\\ \\ \end{align}