Simplify 15 root of x^10y^15

$\sqrt[15]{x^{10} y^{15}}$

Step 1

Reorder $x^{10}$ and $y^{15}$ .

$\sqrt[15]{y^{15} x^{10}}$

Step 2

Pull terms out from under the radical.

$y \sqrt[15]{x^{10}}$

Step 3

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

$y \sqrt[15]{{(x^{2})}^{5}}$

Step 4

Rewrite $\sqrt[15]{{(x^{2})}^{5}}$ as $\sqrt[3]{\sqrt[5]{{(x^{2})}^{5}}}$ .

$y \sqrt[3]{\sqrt[5]{{(x^{2})}^{5}}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

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