100 solutions, 700 upvotes problem

Probability Level 3

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

If the above expression is in the form $A^{2016}$ , find $A$ .