Simplify cube root of (x^24)/27

$\sqrt[3]{\frac{x^{24}}{27}}$

Rewrite $x^{24}$ as ${(x^{8})}^{3}$ .

$\sqrt[3]{\frac{{(x^{8})}^{3}}{27}}$

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{\frac{{(x^{8})}^{3}}{3^{3}}}$

Rewrite $\frac{{(x^{8})}^{3}}{3^{3}}$ as ${(\frac{x^{8}}{3})}^{3}$ .

$\sqrt[3]{{(\frac{x^{8}}{3})}^{3}}$

Pull terms out from under the radical, assuming real numbers.

$\frac{x^{8}}{3}$