# A weird tetrahedron? No?

**Geometry**Level 3

If \(V\) can be written in the form of

\[ \large
\frac{2^{\zeta}a^{\alpha}b^{\beta}c^{\gamma} } {144^{\xi}}
\]

where \(\zeta, \alpha, \gamma\) and \(\xi\) are positive integers, what is the value of \( 50\lfloor \zeta + \alpha + \beta + \gamma + \xi \rfloor \)?