2002 AMC 10P Problem 12

For f_n(x)=x^n and a \neq 1 consider

\text{I. } (f_{11}(a)f_{13}(a))^{14}

\text{II. } f_{11}(a)f_{13}(a)f_{14}(a)

\text{III. } (f_{11}(f_{13}(a)))^{14}

\text{IV. } f_{11}(f_{13}(f_{14}(a)))

Which of these equal f_{2002}(a)?

\text{(A) I and II only} \qquad \text{(B) II and III only} \qquad \text{(C) III and IV only} \qquad \text{(D) II, III, and IV only} \qquad \text{(E) all of them}

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