Simplify the Radical Expression fourth root of (5x)/(16b^4)

$\sqrt[4]{\frac{5 x}{16 b^{4}}}$

Step 1

Rewrite $\frac{5 x}{16 b^{4}}$ as ${(\frac{1}{2 b})}^{4} (5 x)$ .

Factor the perfect power $1^{4}$ out of $5 x$ .

$\sqrt[4]{\frac{1^{4} (5 x)}{16 b^{4}}}$

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

$\sqrt[4]{\frac{1^{4} (5 x)}{{(2 b)}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} (5 x)}{{(2 b)}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{2 b})}^{4} (5 x)}$

Step 2

Pull terms out from under the radical.

$| \frac{1}{2 b} | \sqrt[4]{5 x}$

Step 3

Remove non-negative terms from the absolute value.

$\frac{| 1 |}{2 | b |} \sqrt[4]{5 x}$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{1}{2 | b |} \sqrt[4]{5 x}$

Step 5

Combine $\frac{1}{2 | b |}$ and $\sqrt[4]{5 x}$ .

$\frac{\sqrt[4]{5 x}}{2 | b |}$