Suppose \(f(x)\) is a degree-\(8\) polynomial such that \(f(2^i)=\frac{1}{2^i}\) for all integers \( 0 \leq i \leq 8\). If \(f(0)= \frac{a}{b}\), where \(a\) and \( b\) are coprime positive integers, what is the value of \(a+b?\)

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