Answer
$-\frac{z^{7}}{3x}$
Work Step by Step
$\sqrt[3] (\frac{z^{21}}{27x^{3}})=\frac{z^{7}}{3x}$, because $(\frac{z^{7}}{3x})^{3}=\frac{z^{7}}{3x}\times\frac{z^{7}}{3x}\times \frac{z^{7}}{3x}=\frac{z^{7+7+7}}{(3\times3\times3)\times x^{1+1+1}}=\frac{z^{21}}{27x^{3}}$
Therefore, $-\sqrt[3] (\frac{z^{21}}{27x^{3}})=-\frac{z^{7}}{3x}$. We are just taking the opposite of $\sqrt[3] (\frac{z^{21}}{27x^{3}})$
