Problem 01 | First Shifting Property of Laplace Transform

$\mathcal{L}(t^n) = \dfrac{n!}{s^{n + 1}}$

$\mathcal{L}(t^3) = \dfrac{3!}{s^{3 + 1}}$

$\mathcal{L}(t^3) = \dfrac{6}{s^4}$
 

Thus,
$\mathcal{L}(e^{2t}t^3) = \dfrac{6}{(s - 2)^4}$           answer