AMC 12 2018a Problem 7

For how many (not necessarily positive) integer values of $n$ is the value of $4000\cdot \left(\tfrac{2}{5}\right)^n$ an integer?

$\textbf{(A) }3 \textbf{(B) }4 \textbf{(C) }6 \textbf{(D) }8 \textbf{(E) }9$