Trigonometry Examples

$2 (- \frac{1}{\sqrt{65}}) (- \frac{8}{\sqrt{65}})$

Step 1

Multiply $\frac{1}{\sqrt{65}}$ by $\frac{\sqrt{65}}{\sqrt{65}}$ .

$2 (- (\frac{1}{\sqrt{65}} \cdot \frac{\sqrt{65}}{\sqrt{65}})) \cdot (- \frac{8}{\sqrt{65}})$

Step 2

Combine and simplify the denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{1}{\sqrt{65}}$ by $\frac{\sqrt{65}}{\sqrt{65}}$ .

$2 (- \frac{\sqrt{65}}{\sqrt{65} \sqrt{65}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.2

Raise $\sqrt{65}$ to the power of $1$ .

$2 (- \frac{\sqrt{65}}{{\sqrt{65}}^{1} \sqrt{65}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.3

Raise $\sqrt{65}$ to the power of $1$ .

$2 (- \frac{\sqrt{65}}{{\sqrt{65}}^{1} {\sqrt{65}}^{1}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.4

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

$2 (- \frac{\sqrt{65}}{{\sqrt{65}}^{1 + 1}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.5

Add $1$ and $1$ .

$2 (- \frac{\sqrt{65}}{{\sqrt{65}}^{2}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6

Rewrite ${\sqrt{65}}^{2}$ as $65$ .

Tap for more steps...

Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{65}$ as $65^{\frac{1}{2}}$ .

$2 (- \frac{\sqrt{65}}{{(65^{\frac{1}{2}})}^{2}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6.2

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

$2 (- \frac{\sqrt{65}}{65^{\frac{1}{2} \cdot 2}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6.3

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

$2 (- \frac{\sqrt{65}}{65^{\frac{2}{2}}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.6.4.1

Cancel the common factor.

$2 (- \frac{\sqrt{65}}{65^{\frac{2}{2}}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6.4.2

Rewrite the expression.

$2 (- \frac{\sqrt{65}}{65^{1}}) \cdot (- \frac{8}{\sqrt{65}})$

Step 2.6.5

Evaluate the exponent.

$2 (- \frac{\sqrt{65}}{65}) \cdot (- \frac{8}{\sqrt{65}})$

Step 3

Multiply $2 (- \frac{\sqrt{65}}{65})$ .

Tap for more steps...

Step 3.1

Multiply $- 1$ by $2$ .

$- 2 \frac{\sqrt{65}}{65} \cdot (- \frac{8}{\sqrt{65}})$

Step 3.2

Combine $- 2$ and $\frac{\sqrt{65}}{65}$ .

$\frac{- 2 \sqrt{65}}{65} \cdot (- \frac{8}{\sqrt{65}})$

Step 4

Cancel the common factor of $\sqrt{65}$ .

Tap for more steps...

Step 4.1

Move the leading negative in $- \frac{8}{\sqrt{65}}$ into the numerator.

$\frac{- 2 \sqrt{65}}{65} \cdot \frac{- 8}{\sqrt{65}}$

Step 4.2

Factor $\sqrt{65}$ out of $- 2 \sqrt{65}$ .

$\frac{\sqrt{65} \cdot - 2}{65} \cdot \frac{- 8}{\sqrt{65}}$

Step 4.3

Cancel the common factor.

$\frac{\sqrt{65} \cdot - 2}{65} \cdot \frac{- 8}{\sqrt{65}}$

Step 4.4

Rewrite the expression.

$\frac{- 2}{65} \cdot - 8$

Step 5

Combine $\frac{- 2}{65}$ and $- 8$ .

$\frac{- 2 \cdot - 8}{65}$

Step 6

Multiply $- 2$ by $- 8$ .

$\frac{16}{65}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{65}$

Decimal Form:

$0.2\overline{461538}$