2013 AMC8 Problem 15

theory

algebra geometry
#1
If \(3^p + 3^4 = 90\), \(2^r + 44 = 76\), and \(5^3 + 6^s = 1421\), what is the product of \(p\), \(r\), and \(s\)?

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