2000 AMC 10 Problem 2

Write the factor $2000$ as $2000^1.$ Then $$\begin{aligned} 2000^1 \cdot 2000^{2000} &= 2000^{1 + 2000} \\ &= 2000^{2001}. \end{aligned}$$ Each of the other options is larger than $2000^{2001}.$ Thus, the correct answer is A.