  Studies about the set of positive equilibria ($E_+$) of kinetic systems have
been focused on mass action, and not that much on power law kinetic (PLK)
systems, even for PL-RDK systems (PLK systems where two reactions with
identical reactant complexes have the same kinetic order vectors). For mass
action, reactions with different reactants have different kinetic order rows. A
PL-RDK system satisfying this property is called factor span surjective
(PL-FSK). In this work, we show that a cycle terminal PL-FSK system with
$E_+\ne \varnothing$ and has independent linkage classes (ILC) is a poly-PLP
system, i.e., $E_+$ is the disjoint union of log-parametrized sets. The key
insight for the extension is that factor span surjectivity induces an
isomorphic digraph structure on the kinetic complexes. The result also
completes, for ILC networks, the structural analysis of the original complex
balanced generalized mass action systems (GMAS) by M\"uller and Regensburger.
We also identify a large set of PL-RDK systems where non-emptiness of $E_+$ is
a necessary and sufficient condition for non-emptiness of each set of positive
equilibria for each linkage class. These results extend those of Boros on mass
action systems with ILC. We conclude this paper with two applications of our
results. Firstly, we consider absolute complex balancing (ACB), i.e., the
property that each positive equilibrium is complex balanced, in poly-PLP
systems. Finally, we use the new results to study absolute concentration
robustness (ACR) in these systems. In particular, we obtain a species
hyperplane containment criterion to determine ACR in the system species.
