Simplify fourth root of (x^3)/16

$\sqrt[4]{\frac{x^{3}}{16}}$

Step 1

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

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

$\sqrt[4]{\frac{1^{4} x^{3}}{16}}$

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

$\sqrt[4]{\frac{1^{4} x^{3}}{2^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} x^{3}}{2^{4} \cdot 1}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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