AMC 8 2013 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 $s$? $\textbf{(A)}\ 27 \textbf{(B)}\ 40 \textbf{(C)}\ 50 \textbf{(D)}\ 70 \textbf{(E)}\ 90$