Evaluate -1/2*(-2/( square root of 3))

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

Step 1

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2}{\sqrt{3}}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 5

Multiply $- 1 (- \frac{\sqrt{3}}{3})$ .

Multiply $- 1$ by $- 1$ .

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

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$

Evaluate -1/2*(-2/( square root of 3))

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