Simplify ( square root of 3xy)^3

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

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

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

Apply the product rule to $3 x y$ .

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

Apply the product rule to $3 x$ .

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

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

$\sqrt{27 x^{3} y^{3}}$

Rewrite $27 x^{3} y^{3}$ as ${(3 x y)}^{2} \cdot (3 x y)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{3} y^{3}}$

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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