A Hardy type inequality for Reproducing Kernel Hilbert Space operators is proved. It is well known (see Halmos in A Hilbert space problem book. Springer, Berlin, 1982) the following power inequality for numerical radius of Hilbert space operator A: for any integer . Hovewer, the inverse inequalities for some operator classes with some constant , apparently, are not well investigated in the literature. The same inequalities for the Berezin number of operators on the reproducing Kernel Hilbert space are not studied in general. Here we prove some power inequalities for Berezin number of some operators.