AMC 10 2019a Problem 1

What is the value of $$2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9\,?$$ $\textbf{(A) } 0 \textbf{(B) } 1 \textbf{(C) } 2 \textbf{(D) } 3 \textbf{(E) } 4$