Simplify ${\left({\left(\frac{2}{5}\right)}^2\right)}^{-1}$. Give the answer as a fraction.

Power of a power: ${\left({\left(\frac{2}{5}\right)}^2\right)}^{-1}={\left(\frac{2}{5}\right)}^{2\times (-1)}={\left(\frac{2}{5}\right)}^{-2}={\left(\frac{5}{2}\right)}^2=\frac{25}{4}$. Forgetting to flip the fraction leaves $\frac{4}{25}$, and a negative exponent never makes the result negative.