Simplify cube root of x^9y^16

$\sqrt[3]{x^{9} y^{16}}$

Step 1

Rewrite $x^{9} y^{16}$ as ${(x^{3} y^{5})}^{3} y$ .

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

$\sqrt[3]{{(x^{3})}^{3} y^{16}}$

Factor out $y^{15}$ .

$\sqrt[3]{{(x^{3})}^{3} (y^{15} y)}$

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

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

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

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

Step 2

Pull terms out from under the radical.

$x^{3} y^{5} \sqrt[3]{y}$