Pre-Algebra Examples

$\sqrt[3]{\frac{1}{512}}$

Step 1

Rewrite $\sqrt[3]{\frac{1}{512}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{512}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{512}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{512}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $512$ as $8^{3}$ .

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

Step 3.2

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

$\frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$