**EDIT** $:$

Consider the vector space $\mathbb R$ over the field $\mathbb Q$.Consider the irrational number $e$ and let $c\_1 , c\_2 , ... , c\_n$ be distinct rational numbers.Then show that $e^{c\_{1}} ,e^{c\_{2}} ,... , e^{c\_{n}}$ are linearly independent.

I have tried but I fail.Please help me.

Thank you in advance.