Answer
$-3z\sqrt[5] (z^{4})$
Work Step by Step
$\sqrt [5] (-243z^{9})=\sqrt [5] (-243\times z^{5}\times z^{4})$
$=\sqrt [5] (-243)\times \sqrt[5] (z^{5})\times \sqrt[5] (z^{4})=-3z\sqrt[5] (z^{4})$
We know that $\sqrt[5] (-243)=-3$, because $(-3)^{5}=-243$ and also that $\sqrt[5] (z^{5})=z$, because $(z)^{5}=z^{5}$.
