Simplify fifth root of y^1625 root of y^2*0

$\sqrt[5]{y^{16}} \sqrt[25]{y^{2} \cdot 0}$

Rewrite $y^{16}$ as ${(y^{3})}^{5} y$ .

Factor out $y^{15}$ .

$\sqrt[5]{y^{15} y} \sqrt[25]{y^{2} \cdot 0}$

Rewrite $y^{15}$ as ${(y^{3})}^{5}$ .

$\sqrt[5]{{(y^{3})}^{5} y} \sqrt[25]{y^{2} \cdot 0}$

Pull terms out from under the radical.

$y^{3} \sqrt[5]{y} \sqrt[25]{y^{2} \cdot 0}$

Write the expression using exponents.

Multiply $y^{2}$ by $0$ .

$y^{3} \sqrt[5]{y} \sqrt[25]{0}$

Rewrite $0$ as $0^{25}$ .

$y^{3} \sqrt[5]{y} \sqrt[25]{0^{25}}$

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

$y^{3} \sqrt[5]{y} \cdot 0$

Multiply $y^{3} \sqrt[5]{y} \cdot 0$ .

Multiply $0$ by $y^{3}$ .

$0 \sqrt[5]{y}$

Multiply $0$ by $\sqrt[5]{y}$ .

$0$