Simplify ( cube root of 27x^3y)( cube root of x^3y)

$(\sqrt[3]{27 x^{3} y}) (\sqrt[3]{x^{3} y})$

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

Rewrite $27$ as $3^{3}$ .

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

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

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

Pull terms out from under the radical.

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

Pull terms out from under the radical.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Raise $\sqrt[3]{y}$ to the power of $1$ .

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

Raise $\sqrt[3]{y}$ to the power of $1$ .

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

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

$3 x^{2} {\sqrt[3]{y}}^{1 + 1}$

Add $1$ and $1$ .

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

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

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