Trigonometry Examples

$2 (\frac{\sqrt{26}}{26}) (- \frac{5 \sqrt{26}}{26})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Move the leading negative in $- \frac{5 \sqrt{26}}{26}$ into the numerator.

$2 (\frac{\sqrt{26}}{26}) \cdot \frac{- 5 \sqrt{26}}{26}$

Step 1.2

Factor $2$ out of $26$ .

$2 (\frac{\sqrt{26}}{26}) \cdot \frac{- 5 \sqrt{26}}{2 (13)}$

Step 1.3

Cancel the common factor.

$2 \frac{\sqrt{26}}{26} \cdot \frac{- 5 \sqrt{26}}{2 \cdot 13}$

Step 1.4

Rewrite the expression.

$\frac{\sqrt{26}}{26} \cdot \frac{- 5 \sqrt{26}}{13}$

Step 2

Multiply $\frac{\sqrt{26}}{26}$ by $\frac{- 5 \sqrt{26}}{13}$ .

$\frac{\sqrt{26} (- 5 \sqrt{26})}{26 \cdot 13}$

Step 3

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{- 5 ({\sqrt{26}}^{1} \sqrt{26})}{26 \cdot 13}$

Step 4

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{- 5 ({\sqrt{26}}^{1} {\sqrt{26}}^{1})}{26 \cdot 13}$

Step 5

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

$\frac{- 5 {\sqrt{26}}^{1 + 1}}{26 \cdot 13}$

Step 6

Simplify the expression.

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Step 6.1

Add $1$ and $1$ .

$\frac{- 5 {\sqrt{26}}^{2}}{26 \cdot 13}$

Step 6.2

Multiply $26$ by $13$ .

$\frac{- 5 {\sqrt{26}}^{2}}{338}$

Step 7

Rewrite ${\sqrt{26}}^{2}$ as $26$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{26}$ as $26^{\frac{1}{2}}$ .

$\frac{- 5 {(26^{\frac{1}{2}})}^{2}}{338}$

Step 7.2

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

$\frac{- 5 \cdot 26^{\frac{1}{2} \cdot 2}}{338}$

Step 7.3

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

$\frac{- 5 \cdot 26^{\frac{2}{2}}}{338}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$\frac{- 5 \cdot 26^{\frac{2}{2}}}{338}$

Step 7.4.2

Rewrite the expression.

$\frac{- 5 \cdot 26^{1}}{338}$

Step 7.5

Evaluate the exponent.

$\frac{- 5 \cdot 26}{338}$

Step 8

Multiply $- 5$ by $26$ .

$\frac{- 130}{338}$

Step 9

Cancel the common factor of $- 130$ and $338$ .

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Step 9.1

Factor $26$ out of $- 130$ .

$\frac{26 (- 5)}{338}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $26$ out of $338$ .

$\frac{26 \cdot - 5}{26 \cdot 13}$

Step 9.2.2

Cancel the common factor.

$\frac{26 \cdot - 5}{26 \cdot 13}$

Step 9.2.3

Rewrite the expression.

$\frac{- 5}{13}$

Step 10

Move the negative in front of the fraction.

$- \frac{5}{13}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{13}$

Decimal Form:

$- 0.\overline{384615}$