Precalculus Examples

$- \cot^{2} (\frac{π}{6})$

Step 1

The exact value of $\cot (\frac{π}{6})$ is $\sqrt{3}$ .

$- {\sqrt{3}}^{2}$

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

$- 3^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$- 3^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$- 3^{1}$

Step 2.5

Evaluate the exponent.

$- 1 \cdot 3$

Step 3

Multiply $- 1$ by $3$ .

$- 3$