  Using relations from random matrix theory, we derive exact expressions for
all $n$-point spectral correlation functions of Dirac operator eigenvalues in
terms of finite-volume partition functions. This is done for both chiral
symplectic and chiral unitary random matrix ensembles, which correspond to
$SU(N_c \geq 3)$ gauge theories with $N_f$ fermions in the adjoint and
fundamental representations, respectively. In the latter case we infer from
this an infinite sequence of consistency conditions that must be satisfied by
the corresponding finite-volume partition functions.
