Simplify y^2 cube root of 750x^10y^10

$y^{2} \sqrt[3]{750 x^{10} y^{10}}$

Rewrite $750 x^{10} y^{10}$ as ${(5 x^{3} y^{3})}^{3} \cdot (6 x y)$ .

Factor $125$ out of $750$ .

$y^{2} \sqrt[3]{125 (6) x^{10} y^{10}}$

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

$y^{2} \sqrt[3]{5^{3} \cdot 6 x^{10} y^{10}}$

Factor out $x^{9}$ .

$y^{2} \sqrt[3]{5^{3} \cdot 6 (x^{9} x) y^{10}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$y^{2} \sqrt[3]{5^{3} \cdot 6 ({(x^{3})}^{3} x) y^{10}}$

Factor out $y^{9}$ .

$y^{2} \sqrt[3]{5^{3} \cdot 6 ({(x^{3})}^{3} x) (y^{9} y)}$

Rewrite $y^{9}$ as ${(y^{3})}^{3}$ .

$y^{2} \sqrt[3]{5^{3} \cdot 6 ({(x^{3})}^{3} x) ({(y^{3})}^{3} y)}$

Move $x$ .

$y^{2} \sqrt[3]{5^{3} \cdot 6 ({(x^{3})}^{3}) {(y^{3})}^{3} x y}$

Move $6$ .

$y^{2} \sqrt[3]{(5^{3} ({(x^{3})}^{3})) {(y^{3})}^{3} \cdot 6 x y}$

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

$y^{2} \sqrt[3]{{(5 x^{3} y^{3})}^{3} \cdot 6 x y}$

Add parentheses.

$y^{2} \sqrt[3]{{(5 x^{3} y^{3})}^{3} \cdot 6 (x y)}$

Add parentheses.

$y^{2} \sqrt[3]{{(5 x^{3} y^{3})}^{3} \cdot (6 x y)}$

Pull terms out from under the radical.

$y^{2} (5 x^{3} y^{3} \sqrt[3]{6 x y})$

Rewrite using the commutative property of multiplication.

$5 y^{2} (x^{3} y^{3} \sqrt[3]{6 x y})$

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$5 (y^{3} y^{2}) (x^{3} \sqrt[3]{6 x y})$

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

$5 y^{3 + 2} (x^{3} \sqrt[3]{6 x y})$

Add $3$ and $2$ .

$5 y^{5} (x^{3} \sqrt[3]{6 x y})$

$5 y^{5} x^{3} \sqrt[3]{6 x y}$