Simplify cube root of (x^2)/27

$\sqrt[3]{\frac{x^{2}}{27}}$

Step 1

Rewrite $\frac{x^{2}}{27}$ as ${(\frac{1}{3})}^{3} x^{2}$ .

Factor the perfect power $1^{3}$ out of $x^{2}$ .

$\sqrt[3]{\frac{1^{3} x^{2}}{27}}$

Factor the perfect power $3^{3}$ out of $27$ .

$\sqrt[3]{\frac{1^{3} x^{2}}{3^{3} \cdot 1}}$

Rearrange the fraction $\frac{1^{3} x^{2}}{3^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{1}{3})}^{3} x^{2}}$

Step 2

Pull terms out from under the radical.

$\frac{1}{3} \sqrt[3]{x^{2}}$

Step 3

Combine $\frac{1}{3}$ and $\sqrt[3]{x^{2}}$ .

$\frac{\sqrt[3]{x^{2}}}{3}$