Fix [Formula: see text] and put [Formula: see text]. Improving on results of [M. Skałba, Products of disjoint blocks of consecutive integers which are powers, Colloq. Math. 98 (2003) 1–3], we prove the following. For a given [Formula: see text] and each [Formula: see text], there exists [Formula: see text] such that for any exponent [Formula: see text], there exist nonnegative integers [Formula: see text] satisfying the equation [Formula: see text] and inequalities: [Formula: see text] and [Formula: see text] with [Formula: see text]