Rules of powers of exponents

Question

Why is $e^x \times e^{\ln 2} = e^{x \times \ln 2}$ Not correct?

I thought that if you had something to the power, you could split them E.g $e^4 = e^2.e^2$

Sorry for the lack of latex I find it very confusing to use.

Answer 1

$a^n\cdot b^m = a^{n+m}$. Same follows for exponent.