Algebra Examples

$\sqrt[3]{\frac{216}{512}}$

Step 1

Cancel the common factor of $216$ and $512$ .

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Step 1.1

Factor $8$ out of $216$ .

$\sqrt[3]{\frac{8 (27)}{512}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $512$ .

$\sqrt[3]{\frac{8 \cdot 27}{8 \cdot 64}}$

Step 1.2.2

Cancel the common factor.

$\sqrt[3]{\frac{8 \cdot 27}{8 \cdot 64}}$

Step 1.2.3

Rewrite the expression.

$\sqrt[3]{\frac{27}{64}}$

$\sqrt[3]{\frac{27}{64}}$

$\sqrt[3]{\frac{27}{64}}$

Step 2

Rewrite $\sqrt[3]{\frac{27}{64}}$ as $\frac{\sqrt[3]{27}}{\sqrt[3]{64}}$ .

$\frac{\sqrt[3]{27}}{\sqrt[3]{64}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $27$ as $3^{3}$ .

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

Step 3.2

Pull terms out from under the radical.

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

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $64$ as $4^{3}$ .

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

Step 4.2

Pull terms out from under the radical.

$\frac{3}{4}$

$\frac{3}{4}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$