Question

find the inverse laplace transform of F(s) = 2e^3/s^3

Answer 1

\[F(s)=\frac{2e^3}{s^3}~~?\]
Are you sure about the function? I think you might mean to say \(F(s)=\dfrac{2e^{-3s}}{s^3}\), but I could be wrong.

The Laplace transform of \(f(t)=t^n\) is \(F(s)=\dfrac{n!}{s^{n+1}}\).
Factor out the \(e^3\) and you have
\[f(t)=e^3~t^2\]