$\Large {\dfrac{1}{\pi} e^{2 \ln\left(2\Gamma\left(\frac{3}{2}\right)\right)}} = \ ? \$

This is a part of 10-seconds challenge .

The answer is 1.

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It is quite difficult to solve it in 10 sec but it is a challenge so we have to ...

$\Gamma(\frac{3}{2})$ = $\Gamma(1+\frac{1}{2})$ $= \frac{1}{2}$ $\Gamma(\frac{1}{2})$ $= \frac{\sqrt{\pi}}{2}$

$\frac{1}{\pi} e^{2ln(\sqrt{\pi})} = \frac{1}{\pi} e^{ln(\pi)}=\pi \times \frac{1}{\pi} =\boxed{1}$