Simplify cube root of (162x^5y^8)/(6x^2y^2)

$\sqrt[3]{\frac{162 x^{5} y^{8}}{6 x^{2} y^{2}}}$

Step 1

Reduce the expression $\frac{162 x^{5} y^{8}}{6 x^{2} y^{2}}$ by cancelling the common factors.

Factor $6$ out of $162 x^{5} y^{8}$ .

$\sqrt[3]{\frac{6 (27 x^{5} y^{8})}{6 x^{2} y^{2}}}$

Factor $6$ out of $6 x^{2} y^{2}$ .

$\sqrt[3]{\frac{6 (27 x^{5} y^{8})}{6 (x^{2} y^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{6 (27 x^{5} y^{8})}{6 (x^{2} y^{2})}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{5} y^{8}}{x^{2} y^{2}}}$

Step 2

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

Factor $x^{2}$ out of $27 x^{5} y^{8}$ .

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{8})}{x^{2} y^{2}}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{8})}{x^{2} (y^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (27 x^{3} y^{8})}{x^{2} y^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{3} y^{8}}{y^{2}}}$

Step 3

Cancel the common factor of $y^{8}$ and $y^{2}$ .

Factor $y^{2}$ out of $27 x^{3} y^{8}$ .

$\sqrt[3]{\frac{y^{2} (27 x^{3} y^{6})}{y^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{y^{2} (27 x^{3} y^{6})}{y^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{y^{2} (27 x^{3} y^{6})}{y^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{3} y^{6}}{1}}$

Divide $27 x^{3} y^{6}$ by $1$ .

$\sqrt[3]{27 x^{3} y^{6}}$

Step 4

Rewrite $27 x^{3} y^{6}$ as ${(3 x y^{2})}^{3}$ .

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

Step 5

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

$3 x y^{2}$