Summary: The period of balancing numbers modulo \(m\), denoted by \(\pi(m)\), is the least positive integer \(n\) such that \((B_n, B_{n+1}) \equiv (0, 1)\pmod m\), where \(B_n\) is the \(n\)-th balancing number. While studying periodicity of balancing numbers, G. K. Panda and S. S. Rout [Acta Math. Hung. 143, No. 2, 274–286 (2014; Zbl 1324.11001)] found the results for \(\pi(B_n)\) and \(\pi(P_n)\), where \(P_n\) denotes the \(n\)-th Pell number. In this article we obtain the formulas of \(\pi(B_n^{k+1})\) and \(\pi(P_n^{k+1})\) for all \(k\geq 1\).