Answer
$e^x=e^a[1+(x-a)+\dfrac{(x-a)^2}{2!}+...+\dfrac{(x-a)^n}{n!}]$
Work Step by Step
The Taylor's series for $f(x)$ at $x=a$ is as follows:
$\Sigma_{n=0}^{\infty} \dfrac{f^{k}(a)}{k!}(x-a)^k=f(a)+f'(a)(x-a)+.....+\dfrac{f^{n}(a)}{n!}(x-a)^n$
Therefore, $f(x)=e^x$ and $f^n(a)=e^a$
$e^ x=e^a+e^a(x-a) +e^a \dfrac{(x-a)^2}{2!}+......$
or, $e^x=e^a[1+(x-a)+\dfrac{(x-a)^2}{2!}+...+\dfrac{(x-a)^n}{n!}]$
