Algebra Examples

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

Step 1

Reduce the expression $\frac{8 x}{64}$ by cancelling the common factors.

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Step 1.1

Factor $8$ out of $8 x$ .

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

Step 1.2

Factor $8$ out of $64$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

Rewrite $\frac{x}{8}$ as ${(\frac{1}{2})}^{3} x$ .

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Step 2.1

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

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

Step 2.2

Factor the perfect power $2^{3}$ out of $8$ .

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

Step 2.3

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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