# 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 $$p_1+p_2+\alpha+\beta$$.

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