Evaluate e^(-2 natural log of 1/5)

$e^{- 2 \ln (\frac{1}{5})}$

Simplify $- 2 \ln (\frac{1}{5})$ by moving $- 2$ inside the logarithm.

$e^{\ln ({(\frac{1}{5})}^{- 2})}$

Exponentiation and log are inverse functions.

${(\frac{1}{5})}^{- 2}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$5^{2}$

Raise $5$ to the power of $2$ .

$25$