Precalculus Examples

$\sqrt[3]{\frac{x}{8} - 4}$

Step 1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\sqrt[3]{\frac{x}{8} - 4 \cdot \frac{8}{8}}$

Step 2

Combine $- 4$ and $\frac{8}{8}$ .

$\sqrt[3]{\frac{x}{8} + \frac{- 4 \cdot 8}{8}}$

Step 3

Combine the numerators over the common denominator.

$\sqrt[3]{\frac{x - 4 \cdot 8}{8}}$

Step 4

Multiply $- 4$ by $8$ .

$\sqrt[3]{\frac{x - 32}{8}}$

Step 5

Rewrite $\frac{x - 32}{8}$ as ${(\frac{1}{2})}^{3} (x - 32)$ .

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Step 5.1

Factor the perfect power $1^{3}$ out of $x - 32$ .

$\sqrt[3]{\frac{1^{3} (x - 32)}{8}}$

Step 5.2

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

$\sqrt[3]{\frac{1^{3} (x - 32)}{2^{3} \cdot 1}}$

Step 5.3

Rearrange the fraction $\frac{1^{3} (x - 32)}{2^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{1}{2})}^{3} (x - 32)}$

Step 6

Pull terms out from under the radical.

$\frac{1}{2} \sqrt[3]{x - 32}$

Step 7

Combine $\frac{1}{2}$ and $\sqrt[3]{x - 32}$ .

$\frac{\sqrt[3]{x - 32}}{2}$