We have:$$e^{2\pi\cdot i(1+\frac{1}{x})}$$
Power properties state that: $a^{b\cdot c}=(a^{b})^{c}=(a^{c})^{b}$. Thus we could re-write the above power as: $$(e^{2\pi\cdot i})^{1+\frac{1}{x}}=1$$ Which should be equal to: $$(e^{1+\frac{1}{x}})^{2\pi\cdot i}\neq1$$ But this is not the case. Also the first result is a Real number while the second is a Complex one.
I'm not really questioning anything, I just couldn't find the right title. Can anyone explain me where the mistake is?
