why does e^-400 = 0?

e^-400 is a number by a negative exponent; therefore, it has to be inverted in order to have a positive exponent. This works out to be $${\frac{{\mathtt{1}}}{{{\mathtt{e}}}^{{\mathtt{400}}}}}$$

 

This number is so fantastically miniscule that, instead of writing it out, it is just presented as 'zero'.