2014 AMC 12A Problem 7

The first three terms of a geometric progression are \sqrt 3, \sqrt[3]3, and \sqrt[6]3. What is the fourth term?

\textbf{(A) }1\qquad \textbf{(B) }\sqrt[7]3\qquad \textbf{(C) }\sqrt[8]3\qquad \textbf{(D) }\sqrt[9]3\qquad \textbf{(E) }\sqrt[10]3\qquad

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