Simplify (e^(-x/2))^2

${(e^{- \frac{x}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$e^{- \frac{x}{2} \cdot 2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$e^{\frac{- x}{2} \cdot 2}$

Cancel the common factor.

$e^{\frac{- x}{2} \cdot 2}$

Rewrite the expression.

$e^{- x}$