Trigonometry Examples

$\frac{4}{- 3 \sqrt{11}}$

Step 1

Move the negative in front of the fraction.

$- \frac{4}{3 \sqrt{11}}$

Step 2

Multiply $\frac{4}{3 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$- (\frac{4}{3 \sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}})$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{4}{3 \sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$- \frac{4 \sqrt{11}}{3 \sqrt{11} \sqrt{11}}$

Step 3.2

Move $\sqrt{11}$ .

$- \frac{4 \sqrt{11}}{3 (\sqrt{11} \sqrt{11})}$

Step 3.3

Raise $\sqrt{11}$ to the power of $1$ .

$- \frac{4 \sqrt{11}}{3 ({\sqrt{11}}^{1} \sqrt{11})}$

Step 3.4

Raise $\sqrt{11}$ to the power of $1$ .

$- \frac{4 \sqrt{11}}{3 ({\sqrt{11}}^{1} {\sqrt{11}}^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{4 \sqrt{11}}{3 {\sqrt{11}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$- \frac{4 \sqrt{11}}{3 {\sqrt{11}}^{2}}$

Step 3.7

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$- \frac{4 \sqrt{11}}{3 {(11^{\frac{1}{2}})}^{2}}$

Step 3.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{4 \sqrt{11}}{3 \cdot 11^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine $\frac{1}{2}$ and $2$ .

$- \frac{4 \sqrt{11}}{3 \cdot 11^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$- \frac{4 \sqrt{11}}{3 \cdot 11^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$- \frac{4 \sqrt{11}}{3 \cdot 11^{1}}$

Step 3.7.5

Evaluate the exponent.

$- \frac{4 \sqrt{11}}{3 \cdot 11}$

Step 4

Multiply $3$ by $11$ .

$- \frac{4 \sqrt{11}}{33}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 \sqrt{11}}{33}$

Decimal Form:

$- 0.40201512 \dots$