2013 AMC8 Problem 15

theory

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

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