Simplify cube root of x/64

$\sqrt[3]{\frac{x}{64}}$

Step 1

Rewrite $\frac{x}{64}$ as ${(\frac{1}{4})}^{3} x$ .

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

$\sqrt[3]{\frac{1^{3} x}{64}}$

Factor the perfect power $4^{3}$ out of $64$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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