The radio k-chromatic number rc_k(G) of a graph G is the minimum integer λ such that there exists a function ϕ:V(G)→{0,1,⋯,λ} satisfying |ϕ(u)−ϕ(v)|≥k+1−d(u,v), where d(u, v) denotes the distance between u and v. To date, several upper and lower bounds of rc_k(⋅) is established for different graph families. One of the most notable works in this domain is due to Liu and Zhu [SIAM Journal on Discrete Mathematics 2005] whose main results were computing the exact values of rc_k(⋅) for paths and cycles for the specific case when k is equal to the diameter. In this article, we find the exact values of rc_k(G) for powers of paths where the diameter of the graph is strictly less than k. Our proof readily provides a linear time algorithm for providing such labeling. Furthermore, our proof technique is a potential tool for solving the same problem for other graph classes with “small” diameter.