Simplify fourth root of (3a)/(16b^8)

$\sqrt[4]{\frac{3 a}{16 b^{8}}}$

Step 1

Rewrite $\frac{3 a}{16 b^{8}}$ as ${(\frac{1}{2 b^{2}})}^{4} (3 a)$ .

Factor the perfect power $1^{4}$ out of $3 a$ .

$\sqrt[4]{\frac{1^{4} (3 a)}{16 b^{8}}}$

Factor the perfect power ${(2 b^{2})}^{4}$ out of $16 b^{8}$ .

$\sqrt[4]{\frac{1^{4} (3 a)}{{(2 b^{2})}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} (3 a)}{{(2 b^{2})}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{2 b^{2}})}^{4} (3 a)}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2 b^{2}} \sqrt[4]{3 a}$

Step 3

Combine $\frac{1}{2 b^{2}}$ and $\sqrt[4]{3 a}$ .

$\frac{\sqrt[4]{3 a}}{2 b^{2}}$