In this paper we prove some results concerning annihilators of power values of derivations in prime rings. The following main theorem establishes a unified version of several earlier results in the literature:LetRbe a prime ring with centerZand with extended centroidC,Q, its two-sided Martindale quotient ring, ρ a nonzero right ideal ofRandDa nonzero derivation ofR.Suppose that aD([x,y])n∈Z(D([x,y])na ∈Z) for allx,y∈ρ wherea∈Randnis a fixed positive integer. If [ρ,ρ]ρ ≠ 0 and dimCRC >4, then eitheraD(ρ) = 0 (a = 0 resp.) orD= ad(p) for somep∈Qsuch thatpρ = 0.