\displaystyle[br]\begin{equation*}\left(\frac{1}{81}\right)^{1/3} = \left(\frac{1}{9^2}\right)^{1/3} = (9^{-2})^{1/3} = 9^{-2/3}\end{equation*}
\displaystyle[br]\begin{equation*}\left(\frac{1}{81}\right)^{1/3} = \left(\frac{1}{9^2}\right)^{1/3} = (9^{-2})^{1/3} = 9^{-2/3}\end{equation*}