Evaluate -25^(-1/2)

$- 25^{- \frac{1}{2}}$

Step 1

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

$- \frac{1}{25^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$- \frac{1}{{(5^{2})}^{\frac{1}{2}}}$

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

$- \frac{1}{5^{2 (\frac{1}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{1}{5^{2 (\frac{1}{2})}}$

Rewrite the expression.

$- \frac{1}{5^{1}}$

Evaluate the exponent.

$- \frac{1}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{5}$

Decimal Form:

$- 0.2$