Simplify fourth root of 27/(x^8)

$\sqrt[4]{\frac{27}{x^{8}}}$

Step 1

Rewrite $\frac{27}{x^{8}}$ as ${(\frac{1}{x^{2}})}^{4} \cdot 27$ .

Factor the perfect power $1^{4}$ out of $27$ .

$\sqrt[4]{\frac{1^{4} \cdot 27}{x^{8}}}$

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

$\sqrt[4]{\frac{1^{4} \cdot 27}{{(x^{2})}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} \cdot 27}{{(x^{2})}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{x^{2}})}^{4} \cdot 27}$

Step 2

Pull terms out from under the radical.

$\frac{1}{x^{2}} \sqrt[4]{27}$

Step 3

Combine $\frac{1}{x^{2}}$ and $\sqrt[4]{27}$ .

$\frac{\sqrt[4]{27}}{x^{2}}$