Proof that $e^n$ can not be expressed as a weighted sum of other powers of $e$

Question

How can I prove that $$e^n \neq \sum_{i=0, i\neq n }^{+\infty}k_ie^{i} $$ where e is the base of the natural logarithm, $k_i$ are non-negative integers, and $n$ is a positive integer?