Simplify y cube root of 750x^3y^7

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

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

Factor $125$ out of $750$ .

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

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

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

Factor out $y^{6}$ .

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

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

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

Move $6$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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