# This should've been mechanics!

**Calculus**Level 5

\[ \sqrt{\dfrac{L^{\alpha}}{\pi^{\beta}g^{\gamma}}}\Gamma^{\delta}\left(\dfrac{1}{\eta}\right) \]

where \(\Gamma\) is the gamma function and \(\alpha\), \(\beta\), \(\gamma\), \(\delta\), and \(\eta \) are all positive integers. Find \(\alpha +\beta +\gamma +\eta^{\delta}\).