Precalculus Examples

$\frac{- 1}{\frac{\sqrt{3}}{\frac{2}{\frac{- 1}{2}}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{\frac{2}{\frac{- 1}{2}}}{\sqrt{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{2}{\frac{- 1}{2}} \cdot \frac{1}{\sqrt{3}})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Divide $2$ by $- 1$ .

$- (2 \cdot - 2 \frac{1}{\sqrt{3}})$

Step 5

Multiply $2$ by $- 2$ .

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

Step 6

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 7.2

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 7.3

Raise $\sqrt{3}$ to the power of $1$ .

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

Step 7.4

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

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

Step 7.5

Add $1$ and $1$ .

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

Step 7.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 7.6.2

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

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

Step 7.6.3

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

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

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

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

Step 7.6.4.2

Rewrite the expression.

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

Step 7.6.5

Evaluate the exponent.

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

Step 8

Combine $- 4$ and $\frac{\sqrt{3}}{3}$ .

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Multiply $- - \frac{4 \sqrt{3}}{3}$ .

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Step 10.1

Multiply $- 1$ by $- 1$ .

$1 \frac{4 \sqrt{3}}{3}$

Step 10.2

Multiply $\frac{4 \sqrt{3}}{3}$ by $1$ .

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

Step 11

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.30940107 \dots$