Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.