AHSME 1999 Problem 13

Define a sequence of real numbers $a_1$, $a_2$, $a_3$, $\dots$ by $a_1 = 1$ and $a_{n + 1}^3 = 99a_n^3$ for all $n \geq 1$. Then $a_{100}$ equals $\textbf{(A)}\ 33^{33} \textbf{(B)}\ 33^{99} \textbf{(C)}\ 99^{33} \textbf{(D)}\ 99^{99} \textbf{(E)}\ \text{none of these}$