Reason what 2^k in a sigma will do I am trying to solve the following calculation without a calculator:
$$\sum_{k=0}^82^k{8\choose k}$$
The first part: 
$$\sum_{k=0}^8{8\choose k}$$
is equal to $2^8$. I already know that the answer will be $3^8$. How did the $2^k$ transform the answer from $2^8$ to $3^8$?

$$(x+1)^8= \binom{8}{0}+\binom{8}{1}x+\binom{8}{2}x^2+\cdots+\binom{8}{8}x^8$$
Let $x=2$ and we are done.
