Answer
$2^n$, see explanations.
Work Step by Step
Step 1. Find the sums $S_n$ for different $n$-values: $S_1=2=2^1, S_2=4=2^2, S_3=8=2^3, S_4=16=2^4, S_5=32=2^5, ...$
Step 2. The sum of the $n$th row is given by $S_n=2^n$
Ste[ 3. Expand $(1+1)^n$ using Binomial Theorem (omitting all $1^r$ terms): $(1+1)^n=\begin{pmatrix} n\\0 \end{pmatrix}+\begin{pmatrix} n\\1 \end{pmatrix}+\begin{pmatrix} n\\2 \end{pmatrix}+...+\begin{pmatrix} n\\n \end{pmatrix}=S_n$. Thus we have $S_n=(1+1)^n=2^n$
