The product of all solutions of the equation \[ e^{5(\log_e{x})^2 + 3} = x^8, \quad x > 0 \] is: \begin{enumerate} \item \( e^{\frac{8}{5}} \) \item \( e^{\frac{6}{5}} \) \item \( e^{2} \) \item \( e \) \end{enumerate}