Simplify ( cube root of x^8y^4)/( cube root of x^2y)

$\frac{\sqrt[3]{x^{8} y^{4}}}{\sqrt[3]{x^{2} y}}$

Step 1

Combine $\sqrt[3]{x^{8} y^{4}}$ and $\sqrt[3]{x^{2} y}$ into a single radical.

$\sqrt[3]{\frac{x^{8} y^{4}}{x^{2} y}}$

Step 2

Reduce the expression $\frac{x^{8} y^{4}}{x^{2} y}$ by cancelling the common factors.

Factor $x^{2}$ out of $x^{8} y^{4}$ .

$\sqrt[3]{\frac{x^{2} (x^{6} y^{4})}{x^{2} y}}$

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

$\sqrt[3]{\frac{x^{2} (x^{6} y^{4})}{x^{2} (y)}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (x^{6} y^{4})}{x^{2} y}}$

Rewrite the expression.

$\sqrt[3]{\frac{x^{6} y^{4}}{y}}$

Step 3

Cancel the common factor of $y^{4}$ and $y$ .

Factor $y$ out of $x^{6} y^{4}$ .

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

Cancel the common factors.

Raise $y$ to the power of $1$ .

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

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

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

Step 5

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

$x^{2} y$