Trigonometry Examples

$2 (\frac{3 \sqrt{13}}{13}) (\frac{2 \sqrt{13}}{13})$

Step 1

Multiply $2 (\frac{3 \sqrt{13}}{13})$ .

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Step 1.1

Combine $2$ and $\frac{3 \sqrt{13}}{13}$ .

$\frac{2 (3 \sqrt{13})}{13} \cdot \frac{2 \sqrt{13}}{13}$

Step 1.2

Multiply $3$ by $2$ .

$\frac{6 \sqrt{13}}{13} \cdot \frac{2 \sqrt{13}}{13}$

Step 2

Multiply $\frac{6 \sqrt{13}}{13} \cdot \frac{2 \sqrt{13}}{13}$ .

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Step 2.1

Multiply $\frac{6 \sqrt{13}}{13}$ by $\frac{2 \sqrt{13}}{13}$ .

$\frac{6 \sqrt{13} (2 \sqrt{13})}{13 \cdot 13}$

Step 2.2

Multiply $2$ by $6$ .

$\frac{12 \sqrt{13} \sqrt{13}}{13 \cdot 13}$

Step 2.3

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{12 ({\sqrt{13}}^{1} \sqrt{13})}{13 \cdot 13}$

Step 2.4

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{12 ({\sqrt{13}}^{1} {\sqrt{13}}^{1})}{13 \cdot 13}$

Step 2.5

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

$\frac{12 {\sqrt{13}}^{1 + 1}}{13 \cdot 13}$

Step 2.6

Add $1$ and $1$ .

$\frac{12 {\sqrt{13}}^{2}}{13 \cdot 13}$

Step 2.7

Multiply $13$ by $13$ .

$\frac{12 {\sqrt{13}}^{2}}{169}$

Step 3

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\frac{12 {(13^{\frac{1}{2}})}^{2}}{169}$

Step 3.2

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

$\frac{12 \cdot 13^{\frac{1}{2} \cdot 2}}{169}$

Step 3.3

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

$\frac{12 \cdot 13^{\frac{2}{2}}}{169}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$\frac{12 \cdot 13^{\frac{2}{2}}}{169}$

Step 3.4.2

Rewrite the expression.

$\frac{12 \cdot 13^{1}}{169}$

Step 3.5

Evaluate the exponent.

$\frac{12 \cdot 13}{169}$

Step 4

Multiply $12$ by $13$ .

$\frac{156}{169}$

Step 5

Cancel the common factor of $156$ and $169$ .

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Step 5.1

Factor $13$ out of $156$ .

$\frac{13 (12)}{169}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $13$ out of $169$ .

$\frac{13 \cdot 12}{13 \cdot 13}$

Step 5.2.2

Cancel the common factor.

$\frac{13 \cdot 12}{13 \cdot 13}$

Step 5.2.3

Rewrite the expression.

$\frac{12}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{13}$

Decimal Form:

$0.\overline{923076}$