Trigonometry Examples

$\frac{1}{\frac{4 \sqrt{41}}{41}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{41}{4 \sqrt{41}}$

Step 2

Multiply $\frac{41}{4 \sqrt{41}}$ by $1$ .

$\frac{41}{4 \sqrt{41}}$

Step 3

Multiply $\frac{41}{4 \sqrt{41}}$ by $\frac{\sqrt{41}}{\sqrt{41}}$ .

$\frac{41}{4 \sqrt{41}} \cdot \frac{\sqrt{41}}{\sqrt{41}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{41}{4 \sqrt{41}}$ by $\frac{\sqrt{41}}{\sqrt{41}}$ .

$\frac{41 \sqrt{41}}{4 \sqrt{41} \sqrt{41}}$

Step 4.2

Move $\sqrt{41}$ .

$\frac{41 \sqrt{41}}{4 (\sqrt{41} \sqrt{41})}$

Step 4.3

Raise $\sqrt{41}$ to the power of $1$ .

$\frac{41 \sqrt{41}}{4 ({\sqrt{41}}^{1} \sqrt{41})}$

Step 4.4

Raise $\sqrt{41}$ to the power of $1$ .

$\frac{41 \sqrt{41}}{4 ({\sqrt{41}}^{1} {\sqrt{41}}^{1})}$

Step 4.5

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

$\frac{41 \sqrt{41}}{4 {\sqrt{41}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{41 \sqrt{41}}{4 {\sqrt{41}}^{2}}$

Step 4.7

Rewrite ${\sqrt{41}}^{2}$ as $41$ .

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Step 4.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{41}$ as $41^{\frac{1}{2}}$ .

$\frac{41 \sqrt{41}}{4 {(41^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{41 \sqrt{41}}{4 \cdot 41^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{41 \sqrt{41}}{4 \cdot 41^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{41 \sqrt{41}}{4 \cdot 41^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{41 \sqrt{41}}{4 \cdot 41^{1}}$

Step 4.7.5

Evaluate the exponent.

$\frac{41 \sqrt{41}}{4 \cdot 41}$

Step 5

Cancel the common factor of $41$ .

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Step 5.1

Cancel the common factor.

$\frac{41 \sqrt{41}}{4 \cdot 41}$

Step 5.2

Rewrite the expression.

$\frac{\sqrt{41}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{41}}{4}$

Decimal Form:

$1.60078105 \dots$