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1999 AMC 12 Question 13

AMC12 · 1999 AMC 12

Question 13

Define a sequence of real numbers $a_1,$ $a_2,$ $a_3,$ $\ldots$ by $a_1 = 1$ and $a_{n+1}^3 = 99 a_n^3$ for all $n \ge 1.$ Then $a_{100}$ equals
  1. $33^{33}$
  2. $33^{99}$
  3. $99^{33}$
  4. $99^{99}$
  5. none of these