Suppose \(f(x)\) is a degree \(8\) polynomial such that \(f(2^i)=\frac{1}{2^i}\) for all integers \(0≤i≤8\). Evaluate \(f(0)\).

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The text is a little small, what is two to the power of in f(2^[this])?

\[\large f(2^i)=\frac{1}{2^i}\]its \(i\)

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