  We prove a general independent equidistribution result for Gauss sums
associated to $n$ monomials in $r$ variable multiplicative characters over a
finite field, which generalizes several previous equidistribution results for
Gauss and Jacobi sums. As an application, we show that any relation satisfied
by these Gauss sums must be a combination of the conjugation relation
$G(\chi)G(\overline\chi)=\pm q$, Galois conjugation invariance and the
Hasse-Davenport product formula.
