1999 AHSME Problems/Problem 13

Define a sequence of real numbers $a_1$ , $a_2$ , $a_3$ , $\dots$ by $a_1 \equal{} 1$ (Error compiling LaTeX. Unknown error_msg) and $a_{n\plus{}1}^3 \equal{} 99a_n^3$ (Error compiling LaTeX. Unknown error_msg) for all $n \ge� 1$ (Error compiling LaTeX. Unknown error_msg). Then $a_{100}$ equals

$\textbf{(A)}\ 33^{33} \qquad \textbf{(B)}\ 33^{99} \qquad \textbf{(C)}\ 99^{33} \qquad \textbf{(D)}\ 99^{99} \qquad \textbf{(E)}\ \text{none of these}$

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1999 AHSME Problems/Problem 13