Precalculus Examples

$\frac{- 18}{(\sqrt{13}) (2 \sqrt{13})}$

Step 1

Cancel the common factor of $- 18$ and $2$ .

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Step 1.1

Factor $2$ out of $- 18$ .

$\frac{2 \cdot - 9}{\sqrt{13} (2 \sqrt{13})}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $\sqrt{13} (2 \sqrt{13})$ .

$\frac{2 \cdot - 9}{2 (\sqrt{13} (\sqrt{13}))}$

Step 1.2.2

Cancel the common factor.

$\frac{2 \cdot - 9}{2 (\sqrt{13} (\sqrt{13}))}$

Step 1.2.3

Rewrite the expression.

$\frac{- 9}{\sqrt{13} (\sqrt{13})}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{- 9}{{\sqrt{13}}^{1} \sqrt{13}}$

Step 2.2

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{- 9}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}$

Step 2.3

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

$\frac{- 9}{{\sqrt{13}}^{1 + 1}}$

Step 2.4

Add $1$ and $1$ .

$\frac{- 9}{{\sqrt{13}}^{2}}$

Step 3

Simplify by cancelling exponent with radical.

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Step 3.1

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

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Step 3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\frac{- 9}{{(13^{\frac{1}{2}})}^{2}}$

Step 3.1.2

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

$\frac{- 9}{13^{\frac{1}{2} \cdot 2}}$

Step 3.1.3

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

$\frac{- 9}{13^{\frac{2}{2}}}$

Step 3.1.4

Cancel the common factor of $2$ .

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Step 3.1.4.1

Cancel the common factor.

$\frac{- 9}{13^{\frac{2}{2}}}$

Step 3.1.4.2

Rewrite the expression.

$\frac{- 9}{13^{1}}$

Step 3.1.5

Evaluate the exponent.

$\frac{- 9}{13}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{9}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{13}$

Decimal Form:

$- 0.\overline{692307}$