Minimum again?

Algebra Level 5

(a+1a)9+(b+1b)9+(c+1c)9\large\left(a+\dfrac{1}{a}\right)^9 +\left(b+\dfrac{1}{b}\right)^9+\left(c+\dfrac{1}{c}\right)^9

If a,ba,b and cc are positive real numbers such that their sum is 1, find the minimum value of the expression above.

If the minimum value can be expressed as wxyz\dfrac{ w^x}{y^z} for positive integers w,x,yw,x,y and zz, submit your answer as w+x+y+z w+x+y+z.

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