Simplify the Radical Expression - cube root of (z^21)/(27x^3)

$- \sqrt[3]{\frac{z^{21}}{27 x^{3}}}$

Rewrite $z^{21}$ as ${(z^{7})}^{3}$ .

$- \sqrt[3]{\frac{{(z^{7})}^{3}}{27 x^{3}}}$

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$- \sqrt[3]{\frac{{(z^{7})}^{3}}{{(3 x)}^{3}}}$

Rewrite $\frac{{(z^{7})}^{3}}{{(3 x)}^{3}}$ as ${(\frac{z^{7}}{3 x})}^{3}$ .

$- \sqrt[3]{{(\frac{z^{7}}{3 x})}^{3}}$

Pull terms out from under the radical.

$- \frac{z^{7}}{3 x}$