Simplify fifth root of (9x^11y^2)/(32xy^7)

$\sqrt[5]{\frac{9 x^{11} y^{2}}{32 x y^{7}}}$

Step 1

Reduce the expression $\frac{9 x^{11} y^{2}}{32 x y^{7}}$ by cancelling the common factors.

Factor $x$ out of $9 x^{11} y^{2}$ .

$\sqrt[5]{\frac{x (9 x^{10} y^{2})}{32 x y^{7}}}$

Factor $x$ out of $32 x y^{7}$ .

$\sqrt[5]{\frac{x (9 x^{10} y^{2})}{x (32 y^{7})}}$

Cancel the common factor.

$\sqrt[5]{\frac{x (9 x^{10} y^{2})}{x (32 y^{7})}}$

Rewrite the expression.

$\sqrt[5]{\frac{9 x^{10} y^{2}}{32 y^{7}}}$

Step 2

Cancel the common factor of $y^{2}$ and $y^{7}$ .

Factor $y^{2}$ out of $9 x^{10} y^{2}$ .

$\sqrt[5]{\frac{y^{2} (9 x^{10})}{32 y^{7}}}$

Cancel the common factors.

Factor $y^{2}$ out of $32 y^{7}$ .

$\sqrt[5]{\frac{y^{2} (9 x^{10})}{y^{2} (32 y^{5})}}$

Cancel the common factor.

$\sqrt[5]{\frac{y^{2} (9 x^{10})}{y^{2} (32 y^{5})}}$

Rewrite the expression.

$\sqrt[5]{\frac{9 x^{10}}{32 y^{5}}}$

Step 3

Rewrite $\frac{9 x^{10}}{32 y^{5}}$ as ${(\frac{x^{2}}{2 y})}^{5} \cdot 9$ .

Factor the perfect power ${(x^{2})}^{5}$ out of $9 x^{10}$ .

$\sqrt[5]{\frac{{(x^{2})}^{5} \cdot 9}{32 y^{5}}}$

Factor the perfect power ${(2 y)}^{5}$ out of $32 y^{5}$ .

$\sqrt[5]{\frac{{(x^{2})}^{5} \cdot 9}{{(2 y)}^{5} \cdot 1}}$

Rearrange the fraction $\frac{{(x^{2})}^{5} \cdot 9}{{(2 y)}^{5} \cdot 1}$ .

$\sqrt[5]{{(\frac{x^{2}}{2 y})}^{5} \cdot 9}$

Step 4

Pull terms out from under the radical.

$\frac{x^{2}}{2 y} \sqrt[5]{9}$

Step 5

Combine $\frac{x^{2}}{2 y}$ and $\sqrt[5]{9}$ .

$\frac{x^{2} \sqrt[5]{9}}{2 y}$