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Algebra Level 4

Given that \(a,b\) and \(c\) are positive real numbers such that their sum is 18. And the maximum value of \(a^2 b^3 c^4 \) is of the form of \(w^x y^z\) for positive integers \(w,x,y\) and \(z\) with \(w\) and \(y\) as prime numbers. What is the value of \(w+x+y+z\)?

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