Simplify cube root of 8/64

$\sqrt[3]{\frac{8}{64}}$

Step 1

Cancel the common factor of $8$ and $64$ .

Factor $8$ out of $8$ .

$\sqrt[3]{\frac{8 (1)}{64}}$

Cancel the common factors.

Factor $8$ out of $64$ .

$\sqrt[3]{\frac{8 \cdot 1}{8 \cdot 8}}$

Cancel the common factor.

$\sqrt[3]{\frac{8 \cdot 1}{8 \cdot 8}}$

Rewrite the expression.

$\sqrt[3]{\frac{1}{8}}$

Step 2

Rewrite $\sqrt[3]{\frac{1}{8}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{8}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{8}}$

Step 3

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{8}}$

Step 4

Simplify the denominator.

Rewrite $8$ as $2^{3}$ .

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

Pull terms out from under the radical, assuming real numbers.

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$