  Power law systems have been studied extensively due to their wide-ranging
applications, particularly in chemistry. In this work, we focus on power law
systems that can be decomposed into stoichiometrically independent subsystems.
We show that for such systems where the ranks of the augmented matrices
containing the kinetic order vectors of the underlying subnetworks sum up to
the rank of the augmented matrix containing the kinetic order vectors of the
entire network, then the existence of the positive steady states of each
stoichiometrically independent subsystem is a necessary and sufficient
condition for the existence of the positive steady states of the given power
law system. We demonstrate the result through illustrative examples. One of
which is a network of a carbon cycle model that satisfies the assumption, while
the other network fails to meet the assumption. Finally, using the
aforementioned result, we present a systematic method for deriving positive
steady state parametrizations for the mentioned subclass of power law systems,
which is a generalization of our recent method for mass action systems.
