Simplify ( fourth root of 16x^2y^4)/(2xy^5)

$\frac{\sqrt[4]{16 x^{2} y^{4}}}{2 x y^{5}}$

Simplify the numerator.

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

Rewrite $16$ as $2^{4}$ .

$\frac{\sqrt[4]{2^{4} x^{2} y^{4}}}{2 x y^{5}}$

Move $x^{2}$ .

$\frac{\sqrt[4]{2^{4} y^{4} x^{2}}}{2 x y^{5}}$

Rewrite $2^{4} y^{4}$ as ${(2 y)}^{4}$ .

$\frac{\sqrt[4]{{(2 y)}^{4} x^{2}}}{2 x y^{5}}$

Pull terms out from under the radical.

$\frac{2 y \sqrt[4]{x^{2}}}{2 x y^{5}}$

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$\frac{2 y \sqrt{\sqrt{x^{2}}}}{2 x y^{5}}$

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

$\frac{2 y \sqrt{x}}{2 x y^{5}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y \sqrt{x}}{2 x y^{5}}$

Rewrite the expression.

$\frac{y \sqrt{x}}{x y^{5}}$

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

Factor $y$ out of $y \sqrt{x}$ .

$\frac{y (\sqrt{x})}{x y^{5}}$

Cancel the common factors.

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

$\frac{y (\sqrt{x})}{y (x y^{4})}$

Cancel the common factor.

$\frac{y \sqrt{x}}{y (x y^{4})}$

Rewrite the expression.

$\frac{\sqrt{x}}{x y^{4}}$