\[10^{- 1} + 5^{- 2} = \frac{1}{10} + \frac{1}{5^{2}} =\]
\[= \frac{1^{\backslash 5}}{10} + \frac{1^{\backslash 2}}{25} = \frac{5 + 2}{50} = \frac{7}{50}\]