2013 AMC 8 Problem 15

If 3^p + 3^4 = 90, 2^r + 44 = 76, and 5^3 + 6^s = 1421, what is the product of p, r, and s?

\textbf{(A)}\ 27 \qquad \textbf{(B)}\ 40 \qquad \textbf{(C)}\ 50 \qquad \textbf{(D)}\ 70 \qquad \textbf{(E)}\ 90

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