100 solutions, 700 upvotes problem

\[ \dfrac{\binom{2016}{0}+2\binom{2016}{1}+\cdots+2^{2016}\binom{2016}{2016}}{\binom{2016}{0}+\binom{2016}{1}+\cdots+\binom{2016}{2016}}\]

If the above expression is in the form \(A^{2016}\), find \(A\).

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