Simplify fourth root of (x^9y^7)/(xy^3)

$\sqrt[4]{\frac{x^{9} y^{7}}{x y^{3}}}$

Reduce the expression $\frac{x^{9} y^{7}}{x y^{3}}$ by cancelling the common factors.

Factor $x$ out of $x^{9} y^{7}$ .

$\sqrt[4]{\frac{x (x^{8} y^{7})}{x y^{3}}}$

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

$\sqrt[4]{\frac{x (x^{8} y^{7})}{x (y^{3})}}$

Cancel the common factor.

$\sqrt[4]{\frac{x (x^{8} y^{7})}{x y^{3}}}$

Rewrite the expression.

$\sqrt[4]{\frac{x^{8} y^{7}}{y^{3}}}$

Cancel the common factor of $y^{7}$ and $y^{3}$ .

Factor $y^{3}$ out of $x^{8} y^{7}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\sqrt[4]{\frac{y^{3} (x^{8} y^{4})}{y^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{y^{3} (x^{8} y^{4})}{y^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{x^{8} y^{4}}{1}}$

Divide $x^{8} y^{4}$ by $1$ .

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

Rewrite $x^{8} y^{4}$ as ${(x^{2} y)}^{4}$ .

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

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

$x^{2} y$