Simplify fifth root of (x^6)/(y^10)

$\sqrt[5]{\frac{x^{6}}{y^{10}}}$

Step 1

Rewrite $\frac{x^{6}}{y^{10}}$ as ${(\frac{x}{y^{2}})}^{5} x$ .

Factor the perfect power $x^{5}$ out of $x^{6}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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