Answer
$2z^{2}\sqrt[5] (z^{2})$
Work Step by Step
$\sqrt [5] (32z^{12})=\sqrt [5] 32\times\sqrt[5] (z^{10})\times\sqrt[5] (z^{2})=2z^{2}\sqrt[5] (z^{2})$
We know that $\sqrt [5] 32=2$, because $2^{5}=32$. We also know that $\sqrt[5] (z^{10})=z^{2}$, because $(z^{5})^{2}=z^{5\times2}=z^{10}$.
