  The Bernshtein-Kushnirenko-Khovanskii theorem provides a generic root count
for system of Laurent polynomials in terms of the mixed volume of their Newton
polytopes (i.e., the BKK bound). A recent and far-reaching generalization of
this theorem is the study of birationally invariant intersection index by Kaveh
and Khovanskii. This short note establishes a simple geometric condition on the
equality between the BKK bound and the intersection index for a system of
vector spaces of Laurent polynomials. Applying this, we show that the
intersection index for the algebraic Kuramoto equations equals their BKK bound.
