2019 AMC 10A Problem 1

We can evaluate from the top of each exponent tower downward: $$\begin{aligned} &2^{\left(0^{\left(1^9\right)}\right)}\\ &\quad+\left(\left(2^0\right)^1\right)^9\\ &=2^{0^1}+(1^1)^9\\ &=2^0+1^9\\ &=2. \end{aligned}$$ Thus, C is the correct answer.