2016 AMC 12A Problem 18

For some positive integer n, the number 110n^3 has 110 positive integer divisors, including 1 and the number 110n^3. How many positive integer divisors does the number 81n^4 have?

\textbf{(A)}\ 110\qquad\textbf{(B)}\ 191\qquad\textbf{(C)}\ 261\qquad\textbf{(D)}\ 325\qquad\textbf{(E)}\ 425

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.