Simplify: \(\frac{(\sqrt{2}/5)^2}{(\sqrt{2}/5)^{13}}\)
Solution
\[ = \left(\frac{\sqrt{2}}{5}\right)^{2-13} \]
\[ = \left(\frac{\sqrt{2}}{5}\right)^{-11} \]
\[ = \left(\frac{5}{\sqrt{2}}\right)^{11} \]
Final Answer:
\[ \boxed{\left(\frac{5}{\sqrt{2}}\right)^{11}} \]