Maximize it!
Algebra
Level
4
\[\large a^2b^3c^4\]
Positive real numbers \(a\), \(b\) and \(c\) are such that \(a+b+c=18\). If the maximum value of expression above can be written as \(p_1^\alpha \cdot p_2^\beta \), where \(p_1\) and \(p_2\) are prime numbers and \(\alpha\), \(\beta\) are positive integers, find \(p_1+p_2+\alpha+\beta\).
by
Vilakshan Gupta