Simplify fourth root of 32/(x^4)

$\sqrt[4]{\frac{32}{x^{4}}}$

Step 1

Rewrite $\frac{32}{x^{4}}$ as ${(\frac{2}{x})}^{4} \cdot 2$ .

Factor the perfect power $2^{4}$ out of $32$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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