Simplify y cube root of 750x^10y^7

$y \sqrt[3]{750 x^{10} y^{7}}$

Rewrite $750 x^{10} y^{7}$ as ${(5 x^{3} y^{2})}^{3} \cdot (6 x y)$ .

Factor $125$ out of $750$ .

$y \sqrt[3]{125 (6) x^{10} y^{7}}$

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

$y \sqrt[3]{5^{3} \cdot 6 x^{10} y^{7}}$

Factor out $x^{9}$ .

$y \sqrt[3]{5^{3} \cdot 6 (x^{9} x) y^{7}}$

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

$y \sqrt[3]{5^{3} \cdot 6 ({(x^{3})}^{3} x) y^{7}}$

Factor out $y^{6}$ .

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

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

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

Move $x$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

$5 (y^{2} y^{1}) (x^{3} \sqrt[3]{6 x y})$

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

$5 y^{2 + 1} (x^{3} \sqrt[3]{6 x y})$

Add $2$ and $1$ .

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

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