Find the Exact Value e^(-2 natural log of 2)

$e^{- 2 \ln (2)}$

Step 1

Simplify $- 2 \ln (2)$ by moving $- 2$ inside the logarithm.

$e^{\ln (2^{- 2})}$

Step 2

Exponentiation and log are inverse functions.

$2^{- 2}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{2}}$

Step 4

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

$\frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$