Simplify y^2 cube root of 125x^5y^5

$y^{2} \sqrt[3]{125 x^{5} y^{5}}$

Rewrite $125 x^{5} y^{5}$ as ${(5 x y)}^{3} (x^{2} y^{2})$ .

Rewrite $125$ as $5^{3}$ .

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

Factor out $x^{3}$ .

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

Factor out $y^{3}$ .

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

Move $x^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Multiply $y^{2}$ by $y$ by adding the exponents.

Move $y$ .

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

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

Raise $y$ to the power of $1$ .

$5 (y^{1} y^{2}) (x \sqrt[3]{x^{2} y^{2}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 y^{1 + 2} (x \sqrt[3]{x^{2} y^{2}})$

Add $1$ and $2$ .

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

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