Given that 3^8\cdot5^2 \equal{} a^b, where both a and b are positive integers, find the smallest possible value for a \plus{} b.
<spanclass=′latex−bold′>(A)</span>25<spanclass=′latex−bold′>(B)</span>34<spanclass=′latex−bold′>(C)</span>351<spanclass=′latex−bold′>(D)</span>407<spanclass=′latex−bold′>(E)</span>900