Algebra Examples

$f (x) \frac{\sqrt[3]{64 x^{6}}}{x^{5}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $64 x^{6}$ as ${(4 x^{2})}^{3}$ .

$f (x) \frac{\sqrt[3]{{(4 x^{2})}^{3}}}{x^{5}}$

Step 1.2

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

$f (x) \frac{4 x^{2}}{x^{5}}$

$f (x) \frac{4 x^{2}}{x^{5}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x^{2}$ and $x^{5}$ .

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Step 2.1.1

Factor $x^{2}$ out of $4 x^{2}$ .

$f (x) \frac{x^{2} \cdot 4}{x^{5}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $x^{2}$ out of $x^{5}$ .

$f (x) \frac{x^{2} \cdot 4}{x^{2} x^{3}}$

Step 2.1.2.2

Cancel the common factor.

$f (x) \frac{x^{2} \cdot 4}{x^{2} x^{3}}$

Step 2.1.2.3

Rewrite the expression.

$f (x) \frac{4}{x^{3}}$

$f (x) \frac{4}{x^{3}}$

$f (x) \frac{4}{x^{3}}$

Step 2.2

Combine $f (x)$ and $\frac{4}{x^{3}}$ .

$\frac{f (x) \cdot 4}{x^{3}}$

Step 2.3

Move $4$ to the left of $f (x)$ .

$\frac{4 f (x)}{x^{3}}$

$\frac{4 f (x)}{x^{3}}$

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