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Let T = U|T| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with U = |T|. T is said to be class p-wA(s,t) if \[ ( |T^*|^t |T|^2s |T^*|^t )^tps+t ≥ |T^*|^2tp and|T|^2sp ≥ ( |T|^s |T^*|^2t |T|^s )^sps+t \] with 0 < p ≤ 1 and 0 < s, t, s + t ≤ 1. This is a generalization of p-hyponormal or class A operators. In this paper, we shall show that if T belongs to class p-wA(s,t) operator for 0<s,t≤ 1 and 0<p≤ 1, then T^n belongs to class p_1-wA\!(sn,tn) for 0<p_1≤ p and for all positive integer n. As an immediate corollary of this result, we shall also show that if T is a p-w-hyponormal operator, then T^n is also p_1-w-hyponormal for 0<p_1≤ p and for all positive integer n. , number=1, journal=European Journal of Pure and Applied Mathematics, year=2026, month=Feb., pages=6122