Simplify fifth root of 32x^10y^2

$\sqrt[5]{32 x^{10} y^{2}}$

Step 1

Rewrite $32 x^{10} y^{2}$ as ${(2 x^{2})}^{5} y^{2}$ .

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} x^{10} y^{2}}$

Rewrite $x^{10}$ as ${(x^{2})}^{5}$ .

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

Rewrite $2^{5} {(x^{2})}^{5}$ as ${(2 x^{2})}^{5}$ .

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

Step 2

Pull terms out from under the radical.

$2 x^{2} \sqrt[5]{y^{2}}$