Maclaurin Series of $e^{t^2/2}$

Question

How do we find Maclaurin Series of $e^{t^2/2}$? I see one way on one book to do it is applying the fact that $e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}$, then $$e^{t^2/2} = \sum_{n=0}^{\infty}\frac{(\frac{1}{2}t^2)^n}{n!}$$ But I cannot really understand why can we directly subsitute $\frac{1}{2}t^2$ into $e^x$ equation since it is not a constant. May someone explain to me? I am really confused.