  Exponential Puiseux semirings are additive submonoids of $\qq_{\geq 0}$
generated by almost all of the nonnegative powers of a positive rational
number, and they are natural generalizations of rational cyclic semirings. In
this paper, we investigate some of the factorization invariants of exponential
Puiseux semirings and briefly explore the connections of these properties with
semigroup-theoretical invariants. Specifically, we prove that sets of lengths
of atomic exponential Puiseux semirings are almost arithmetic progressions with
a common bound, while unions of sets of lengths are arithmetic progressions.
Additionally, we provide exact formulas to compute the catenary degrees of
these monoids and show that minima and maxima of their sets of distances are
always attained at Betti elements. We conclude by providing various
characterizations of the atomic exponential Puiseux semirings with finite omega
functions; in particular, we completely describe them in terms of their
presentations.
