Simplify fourth root of 16x^5y^11

$\sqrt[4]{16 x^{5} y^{11}}$

Step 1

Rewrite $16 x^{5} y^{11}$ as ${(2 x y^{2})}^{4} (x y^{3})$ .

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} x^{5} y^{11}}$

Factor out $x^{4}$ .

$\sqrt[4]{2^{4} (x^{4} x) y^{11}}$

Factor out $y^{8}$ .

$\sqrt[4]{2^{4} (x^{4} x) (y^{8} y^{3})}$

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

$\sqrt[4]{2^{4} (x^{4} x) ({(y^{2})}^{4} y^{3})}$

Move $x$ .

$\sqrt[4]{2^{4} (x^{4}) {(y^{2})}^{4} x y^{3}}$

Rewrite $2^{4} (x^{4}) {(y^{2})}^{4}$ as ${(2 x y^{2})}^{4}$ .

$\sqrt[4]{{(2 x y^{2})}^{4} x y^{3}}$

Add parentheses.

$\sqrt[4]{{(2 x y^{2})}^{4} (x y^{3})}$

Step 2

Pull terms out from under the radical.

$2 x y^{2} \sqrt[4]{x y^{3}}$