Worked Solution #4 of 5, increasing in difficulty.

Expand the following:

\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large \left ( \ x^{ \frac{4}{3}} \ y^{ - \frac {3}{2} } \ z^{ \frac {1}{4}} \ \right )^{ \frac {5}{2}} \\ \\ &\cssId{Step1}{\Large = x^{ \frac{4 \times 5}{3 \times 2}} \ y^{ - \frac {3 \times 5}{2 \times 2} } \ z^{ \frac {1 \times 5}{4 \times 2}}} \\ \\ &\cssId{Step2}{\Large = x^{ \frac{20}{6}} \ y^{ - \frac {15}{4} } \ z^{ \frac {5}{8}}} \\ \\ &\cssId{Step3}{\Large = x^{ \frac{10}{3}} \ y^{ - \frac {15}{4} } \ z^{ \frac {5}{8}}} \\ \\ \end{align}