Answer
$-\dfrac{1}{5}$
Work Step by Step
Use the rule $a^{-m}=\left(\dfrac{1}{a}\right)^m$:
$-25^{-\frac{1}{2}}=-\left(\frac{1}{25}\right)^{\frac{1}{2}}$
$=-\left(\frac{1}{5^2}\right)^{\frac{1}{2}}$
Use the rule $\left(\dfrac{a}{b}\right)^n=\dfrac{a^m}{b^m}$, then simplify to obtain:
$=-\dfrac{1^{\frac{1}{2}}}{\left(5^2\right)^{ \frac{1}{2}}}$
$=-\dfrac{1}{\left(5^2\right)^{ \frac{1}{2}}}$
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=-\dfrac{1}{5^{2\cdot \frac{1}{2}}}$
$=-\dfrac{1}{5^{1}}$
$=-\dfrac{1}{5}$
Hence, the correct answer is $-\frac{1}{5}$.
