Reduce power formula/ convergence /simplify

Question

I can't seem to be able to simplify this

$$x=(1-2*10^{-23})^{(2*10^{22})}$$

analytically, but it appears to converge to $x = \exp(-.4)$

(The exponent has an exponent.)

Any help is deeply appreciated.

Answer 1

We have $$\exp(a)=\lim_{n \to \infty}\left(1+\frac an\right)^n$$ Your expression is of this form with $n=2\cdot 10^{22}, a=-.4$. As your $n$ is "not too different from infinity" the value should be very close to $\exp(-.4)$ but Alpha gets fooled and returns $1$.