  In this paper, we completely determine the slopes and weights of the
L-functions of an important class of exponential sums arising from analytic
number theory. Our main tools include Adolphson-Sperber's work on toric
exponential sums and Wan's decomposition theorems. One consequence of our main
result is a sharp estimate of these exponential sums. Another consequence is to
obtain an explicit counterexample of Adolphson-Sperber's conjecture on weights
of toric exponential sums.
