Algebra 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 ${(3 i)}^{2}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{1}{{(3 i)}^{1}}$

Step 2.4

Simplify.

$\frac{1}{3 i}$