What is the value of \[2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?\]
$\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4$
$2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9$
$=  1+1 = \boxed{2}$ which corresponds to $\boxed{\text{C}}$.