Worked Solution #5 of 5, increasing in difficulty.

Expand the following:

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