Simplify fifth root of 625/(x^10)

$\sqrt[5]{\frac{625}{x^{10}}}$

Step 1

Rewrite $\frac{625}{x^{10}}$ as ${(\frac{1}{x^{2}})}^{5} \cdot 625$ .

Factor the perfect power $1^{5}$ out of $625$ .

$\sqrt[5]{\frac{1^{5} \cdot 625}{x^{10}}}$

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

$\sqrt[5]{\frac{1^{5} \cdot 625}{{(x^{2})}^{5} \cdot 1}}$

Rearrange the fraction $\frac{1^{5} \cdot 625}{{(x^{2})}^{5} \cdot 1}$ .

$\sqrt[5]{{(\frac{1}{x^{2}})}^{5} \cdot 625}$

Step 2

Pull terms out from under the radical.

$\frac{1}{x^{2}} \sqrt[5]{625}$

Step 3

Combine $\frac{1}{x^{2}}$ and $\sqrt[5]{625}$ .

$\frac{\sqrt[5]{625}}{x^{2}}$