Simplify fourth root of 16x^15y^17

$\sqrt[4]{16 x^{15} y^{17}}$

Step 1

Rewrite $16 x^{15} y^{17}$ as ${(2 x^{3} y^{4})}^{4} (x^{3} y)$ .

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

$\sqrt[4]{2^{4} x^{15} y^{17}}$

Factor out $x^{12}$ .

$\sqrt[4]{2^{4} (x^{12} x^{3}) y^{17}}$

Rewrite $x^{12}$ as ${(x^{3})}^{4}$ .

$\sqrt[4]{2^{4} ({(x^{3})}^{4} x^{3}) y^{17}}$

Factor out $y^{16}$ .

$\sqrt[4]{2^{4} ({(x^{3})}^{4} x^{3}) (y^{16} y)}$

Rewrite $y^{16}$ as ${(y^{4})}^{4}$ .

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

Move $x^{3}$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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