Simplify ( square root of 2xy)^3

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

Rewrite ${\sqrt{2 x y}}^{3}$ as ${({(2 x y)}^{3})}^{\frac{1}{2}}$ .

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

Apply the product rule to $2 x y$ .

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

Apply the product rule to $2 x$ .

$\sqrt{2^{3} x^{3} y^{3}}$

Raise $2$ to the power of $3$ .

$\sqrt{8 x^{3} y^{3}}$

Rewrite $8 x^{3} y^{3}$ as ${(2 x y)}^{2} \cdot (2 x y)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{3} y^{3}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2 x^{3} y^{3}}$

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

$\sqrt{2^{2} \cdot 2 (x^{2} x) (y^{2} y)}$

Move $x$ .

$\sqrt{2^{2} \cdot 2 (x^{2}) y^{2} x y}$

Move $2$ .

$\sqrt{(2^{2} (x^{2})) y^{2} \cdot 2 x y}$

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

$\sqrt{{(2 x y)}^{2} \cdot 2 x y}$

Add parentheses.

$\sqrt{{(2 x y)}^{2} \cdot 2 (x y)}$

Add parentheses.

$\sqrt{{(2 x y)}^{2} \cdot (2 x y)}$

Pull terms out from under the radical.

$2 x y \sqrt{2 x y}$