  Exponential equations in free groups were studied initially by Lyndon and
Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed
that the problem of determining whether or not the class of quadratic
exponential equations have solution is decidable, in finitely generated free
groups. In this paper we show that for finite systems of quadratic exponential
equations decidability passes, under certain hypotheses, from the factor groups
to free products and one-relator products.
