Simplify cube root of (x^9)/27

$\sqrt[3]{\frac{x^{9}}{27}}$

Step 1

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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