How to evaluate the sum $\sum_{k = 0}^{n}2^k {{n}\choose {k}}$

Question

How do I evaluate the sum: $$\sum_{k = 0}^{n}2^k {{n}\choose {k}}$$ I know that $2^k = {n \choose 0} + {n \choose 1} + {n \choose 2} + {n \choose 3}... {n \choose k}$, but I don't know how to proceed from this.

Answer 1

It is known that:

$$(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^ky^{n-k}$$

For $x=2 \text{ and }y=1$: $3^n=\sum_{k=0}^n 2^k \binom{n}{k} $

Answer 2

Hint: $$ (1+x)^n = \sum_{k=0}^n \binom{n}{k} x^k $$