Simplify cube root of (x^15)/(y^6)

$\sqrt[3]{\frac{x^{15}}{y^{6}}}$

Step 1

Rewrite $x^{15}$ as ${(x^{5})}^{3}$ .

$\sqrt[3]{\frac{{(x^{5})}^{3}}{y^{6}}}$

Step 2

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$\sqrt[3]{\frac{{(x^{5})}^{3}}{{(y^{2})}^{3}}}$

Step 3

Rewrite $\frac{{(x^{5})}^{3}}{{(y^{2})}^{3}}$ as ${(\frac{x^{5}}{y^{2}})}^{3}$ .

$\sqrt[3]{{(\frac{x^{5}}{y^{2}})}^{3}}$

Step 4

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

$\frac{x^{5}}{y^{2}}$