Simplify fourth root of (16x^6y^4)/(81x^2y^8)

$\sqrt[4]{\frac{16 x^{6} y^{4}}{81 x^{2} y^{8}}}$

Step 1

Reduce the expression $\frac{16 x^{6} y^{4}}{81 x^{2} y^{8}}$ by cancelling the common factors.

Factor $x^{2}$ out of $16 x^{6} y^{4}$ .

$\sqrt[4]{\frac{x^{2} (16 x^{4} y^{4})}{81 x^{2} y^{8}}}$

Factor $x^{2}$ out of $81 x^{2} y^{8}$ .

$\sqrt[4]{\frac{x^{2} (16 x^{4} y^{4})}{x^{2} (81 y^{8})}}$

Cancel the common factor.

$\sqrt[4]{\frac{x^{2} (16 x^{4} y^{4})}{x^{2} (81 y^{8})}}$

Rewrite the expression.

$\sqrt[4]{\frac{16 x^{4} y^{4}}{81 y^{8}}}$

Step 2

Cancel the common factor of $y^{4}$ and $y^{8}$ .

Factor $y^{4}$ out of $16 x^{4} y^{4}$ .

$\sqrt[4]{\frac{y^{4} (16 x^{4})}{81 y^{8}}}$

Cancel the common factors.

Factor $y^{4}$ out of $81 y^{8}$ .

$\sqrt[4]{\frac{y^{4} (16 x^{4})}{y^{4} (81 y^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{y^{4} (16 x^{4})}{y^{4} (81 y^{4})}}$

Rewrite the expression.

$\sqrt[4]{\frac{16 x^{4}}{81 y^{4}}}$

Step 3

Rewrite $16 x^{4}$ as ${(2 x)}^{4}$ .

$\sqrt[4]{\frac{{(2 x)}^{4}}{81 y^{4}}}$

Step 4

Rewrite $81 y^{4}$ as ${(3 y)}^{4}$ .

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

Step 5

Rewrite $\frac{{(2 x)}^{4}}{{(3 y)}^{4}}$ as ${(\frac{2 x}{3 y})}^{4}$ .

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

Step 6

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

$\frac{2 x}{3 y}$