Worked Solution #2 of 5, increasing in difficulty.

Expand the following:

\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large \root 3 \of { x^{4} \ y^{-3} \ z^{-6} } \\ \\ &\cssId{Step1}{\Large = \left ( \ x^{4} \ y^{-3} \ z^{-6} \right )^{ \frac {1}{3} } }\\ \\ &\cssId{Step2}{\Large = x^{\frac {4}{3}} \ y^{ - \frac {3}{3}} \ z^{ - \frac {6}{3}} }\\ \\ &\cssId{Step3}{\Large = x^{\frac {4}{3}} \ y^{-1} \ z^{-2} }\\ \\ \end{align}