Evaluate 169^(-1/2)

$169^{- \frac{1}{2}}$

Step 1

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

$\frac{1}{169^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

Rewrite $169$ as $13^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{13}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{13}$

Decimal Form:

$0.\overline{076923}$