Determine which of ${\left(\frac{1}{2}e\right)}^{\sqrt{3}}$ and $\left(\sqrt{2}\right)^{\frac{1}{2}\pi}$ is greater.
2. ${\left(\frac{1}{2}e\right)}^{\sqrt{3}}$ = 1.70145654213
$\left(\sqrt{2}\right)^{\frac{1}{2}\pi}$ = 1.72356793413