Simplify cube root of 8x^3y^8

$\sqrt[3]{8 x^{3} y^{8}}$

Step 1

Rewrite $8 x^{3} y^{8}$ as ${(2 x y^{2})}^{3} y^{2}$ .

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} x^{3} y^{8}}$

Factor out $y^{6}$ .

$\sqrt[3]{2^{3} x^{3} (y^{6} y^{2})}$

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

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

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

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

Step 2

Pull terms out from under the radical.

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