Simplify fourth root of 125/(x^8)

$\sqrt[4]{\frac{125}{x^{8}}}$

Step 1

Rewrite $\frac{125}{x^{8}}$ as ${(\frac{1}{x^{2}})}^{4} \cdot 125$ .

Factor the perfect power $1^{4}$ out of $125$ .

$\sqrt[4]{\frac{1^{4} \cdot 125}{x^{8}}}$

Factor the perfect power ${(x^{2})}^{4}$ out of $x^{8}$ .

$\sqrt[4]{\frac{1^{4} \cdot 125}{{(x^{2})}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} \cdot 125}{{(x^{2})}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{x^{2}})}^{4} \cdot 125}$

Step 2

Pull terms out from under the radical.

$\frac{1}{x^{2}} \sqrt[4]{125}$

Step 3

Combine $\frac{1}{x^{2}}$ and $\sqrt[4]{125}$ .

$\frac{\sqrt[4]{125}}{x^{2}}$