Simplify ( cube root of 81x^5y^3)/( cube root of 3x^2)

$\frac{\sqrt[3]{81 x^{5} y^{3}}}{\sqrt[3]{3 x^{2}}}$

Step 1

Combine $\sqrt[3]{81 x^{5} y^{3}}$ and $\sqrt[3]{3 x^{2}}$ into a single radical.

$\sqrt[3]{\frac{81 x^{5} y^{3}}{3 x^{2}}}$

Step 2

Reduce the expression $\frac{81 x^{5} y^{3}}{3 x^{2}}$ by cancelling the common factors.

Factor $3$ out of $81 x^{5} y^{3}$ .

$\sqrt[3]{\frac{3 (27 x^{5} y^{3})}{3 x^{2}}}$

Factor $3$ out of $3 x^{2}$ .

$\sqrt[3]{\frac{3 (27 x^{5} y^{3})}{3 (x^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{3 (27 x^{5} y^{3})}{3 x^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{5} y^{3}}{x^{2}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $27 x^{5} y^{3}$ .

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{3})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{3} y^{3}}{1}}$

Divide $27 x^{3} y^{3}$ by $1$ .

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

Step 4

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

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

Step 5

Pull terms out from under the radical, assuming real numbers.

$3 x y$