1999 AHSME Problem 13

Define a sequence of real numbers a_1, a_2, a_3, \ldots by a_1 = 1 and a_{n+1}^3 = 99a_n^3 for all n \ge 1. Then a_{100} equals

\mathrm{(A) \ } 33^{33} \qquad \mathrm{(B) \ } 33^{99} \qquad \mathrm{(C) \ } 99^{33} \qquad \mathrm{(D) \ }99^{99} \qquad \mathrm{(E) \ none\ of\ the\ above}

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