Simplify (2e^-2)^-4

${(2 e^{- 2})}^{- 4}$

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

${(2 \frac{1}{e^{2}})}^{- 4}$

Combine $2$ and $\frac{1}{e^{2}}$ .

${(\frac{2}{e^{2}})}^{- 4}$

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

${(\frac{e^{2}}{2})}^{4}$

Apply the product rule to $\frac{e^{2}}{2}$ .

$\frac{{(e^{2})}^{4}}{2^{4}}$

Multiply the exponents in ${(e^{2})}^{4}$ .

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

$\frac{e^{2 \cdot 4}}{2^{4}}$

Multiply $2$ by $4$ .

$\frac{e^{8}}{2^{4}}$

Raise $2$ to the power of $4$ .

$\frac{e^{8}}{16}$

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{8}}{16}$

Decimal Form:

$186.30987419 \dots$