Find the Exact Value 9^(-1/2)

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

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

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

Simplify the denominator.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$