Answer
$\frac{1}{5}$
Work Step by Step
We know that $b^{-n}=\frac{1}{b^{n}}$ (where $b$ is a nonzero real number and $n$ is a natural number).
Therefore, $25^{-\frac{1}{2}}=\frac{1}{25^{\frac{1}{2}}}$
Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}=\sqrt[n] a^{m}$ (where $\sqrt[n] a$ is a real number).
Therefore, $\frac{1}{25^{\frac{1}{2}}}=\frac{1}{\sqrt[2] 25^{1}}=\frac{1}{\sqrt 25}=\frac{1}{5}$
We know that $\sqrt 25=5$, because $5^{2}=25$.
