Simplify fourth root of y^13

$\sqrt[4]{y^{13}}$

Step 1

Rewrite $y^{13}$ as ${(y^{3})}^{4} y$ .

Factor out $y^{12}$ .

$\sqrt[4]{y^{12} y}$

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

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

Step 2

Pull terms out from under the radical.

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