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Algebra Level 4

Given that a,ba,b and cc are positive real numbers such that their sum is 18. And the maximum value of a2b3c4a^2 b^3 c^4 is of the form of wxyzw^x y^z for positive integers w,x,yw,x,y and zz with ww and yy as prime numbers. What is the value of w+x+y+zw+x+y+z?

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