Simplify x cube root of 56x^4y^5

$x \sqrt[3]{56 x^{4} y^{5}}$

Rewrite $56 x^{4} y^{5}$ as ${(2 x y)}^{3} \cdot (7 x y^{2})$ .

Factor $8$ out of $56$ .

$x \sqrt[3]{8 (7) x^{4} y^{5}}$

Rewrite $8$ as $2^{3}$ .

$x \sqrt[3]{2^{3} \cdot 7 x^{4} y^{5}}$

Factor out $x^{3}$ .

$x \sqrt[3]{2^{3} \cdot 7 (x^{3} x) y^{5}}$

Factor out $y^{3}$ .

$x \sqrt[3]{2^{3} \cdot 7 (x^{3} x) (y^{3} y^{2})}$

Move $x$ .

$x \sqrt[3]{2^{3} \cdot 7 (x^{3}) y^{3} x y^{2}}$

Move $7$ .

$x \sqrt[3]{(2^{3} (x^{3})) y^{3} \cdot 7 x y^{2}}$

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

$x \sqrt[3]{{(2 x y)}^{3} \cdot 7 x y^{2}}$

Add parentheses.

$x \sqrt[3]{{(2 x y)}^{3} \cdot 7 (x y^{2})}$

Add parentheses.

$x \sqrt[3]{{(2 x y)}^{3} \cdot (7 x y^{2})}$

Pull terms out from under the radical.

$x (2 x y \sqrt[3]{7 x y^{2}})$

Rewrite using the commutative property of multiplication.

$2 x (x y \sqrt[3]{7 x y^{2}})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) (y \sqrt[3]{7 x y^{2}})$

Multiply $x$ by $x$ .

$2 x^{2} (y \sqrt[3]{7 x y^{2}})$

$2 x^{2} y \sqrt[3]{7 x y^{2}}$