Worked Solution #3 of 5, increasing in difficulty.

Expand the following:

\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large \root 3 \of { x^{ - \frac{2}{3}} \ y^{ \frac {3}{4}} \ z^{9} } \\ \\ &\cssId{Step1}{\Large = \left ( \ x^{ - \frac{2}{3}} \ y^{ \frac {3}{4}} \ z^{9} \right )^{ \frac {1}{3} } }\\ \\ &\cssId{Step2}{\Large = x^{ - \frac{2 \times 1}{3 \times3}} \ y^{ \frac {3 \times 1}{4 \times 3}} \ z^{\frac {9 \times 1}{1 \times 3}} }\\ \\ &\cssId{Step3}{\Large = x^{ - \frac{2}{9}} \ y^{ \frac {3}{12}} \ z^{\frac {9}{3}} }\\ \\ &\cssId{Step4}{\Large = x^{ - \frac{2}{9}} \ y^{ \frac {1}{4}} \ z^{3} }\\ \\ \end{align}