Precalculus Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

Evaluate the exponent.

$- \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$