Consider a real valued function \[f(x)\] satisfying ,
\[ 2f(xy)=(f(x))^{y}+(f(y))^{x}\] for all \[x,y \] belonging to the set of real numbers . And \[f(1)=2\] , then find
\[(\sum_{r=1}^{15} f (r))+1000\]

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