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Which Equals our Result?

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April 2, 2013

Problem Statement

For fn(x)=xnf_n(x)=x^n and a≠1a\neq 1 consider
I. (f11(a)f13(a))14(f_{11}(a)f_{13}(a))^{14}
II. f11(a)f13(a)f14(a)f_{11}(a)f_{13}(a)f_{14}(a)
III. (f11(f13(a)))14(f_{11}(f_{13}(a)))^{14}
IV. f11(f13(f14(a)))f_{11}(f_{13}(f_{14}(a)))
Which of these equal f2002(a)f_{2002}(a)?
<spanclass=′latex−bold′>(A)</span>I and II only<spanclass=′latex−bold′>(B)</span>II and III only<spanclass=′latex−bold′>(C)</span>III and IV only<spanclass=′latex−bold′>(D)</span>II, III, and IV only<spanclass=′latex−bold′>(E)</span>all of them<span class='latex-bold'>(A) </span>\text{I and II only}\qquad<span class='latex-bold'>(B) </span>\text{II and III only}\qquad<span class='latex-bold'>(C) </span>\text{III and IV only}\qquad<span class='latex-bold'>(D) </span>\text{II, III, and IV only}\qquad<span class='latex-bold'>(E) </span>\text{all of them}
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