Simplify the Radical Expression cube root of 8x^2y^6

$\sqrt[3]{8 x^{2} y^{6}}$

Step 1

Rewrite $8 x^{2} y^{6}$ as ${(2 y^{2})}^{3} x^{2}$ .

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

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

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

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

Move $x^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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