Simplify (-9)^(-1/2)

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

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.

Rewrite $- 9$ as ${(3 i)}^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{1}{3 i}$