A ?-term is a formal expression obtained from letters of an alphabet using two operations: the binary concatenation and the unary (?-1)-power. A ?-term has a natural interpretation on each finite semigroup S: the concatenation is viewed as the semigroup multiplication while (?-1)-power is interpreted as the unary operation which sends each element s of S to the inverse of ss^? in the maximal subgroup containing its unique idempotent power s^?. The ?-word problem for a class V of finite semigroups consists in deciding whether two ?-terms have the same interpretation over every semigroup of V. We will talk about the ?-word problem for the class of all finite semigroups.