Trigonometry Examples

$\frac{\sqrt{x^{5}}}{\sqrt[3]{x^{3}}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

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Step 1.1.1

Factor out $x^{4}$ .

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

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 2

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

$\frac{x^{2} \sqrt{x}}{x}$

Step 3

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

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Step 3.1

Factor $x$ out of $x^{2} \sqrt{x}$ .

$\frac{x (x \sqrt{x})}{x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $x$ to the power of $1$ .

$\frac{x (x \sqrt{x})}{x^{1}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (x \sqrt{x})}{x \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{x (x \sqrt{x})}{x \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{x \sqrt{x}}{1}$

Step 3.2.5

Divide $x \sqrt{x}$ by $1$ .

$x \sqrt{x}$

$x \sqrt{x}$

$x \sqrt{x}$

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