Distributivity equations of fuzzy implications over triangular norms and triangular conorms play an important role in approximate reasoning, especially in fuzzy reasoning and control. A great deal of researches have been done on the distributivity equations of fuzzy implications over triangular norms and triangular conorms. Recently, Massanet et al. proposed a new kind of fuzzy implications based on powers of continuous t-norms, called T-power based implications and made an in-depth study of its properties. To extend the knowledge system of T-power implications and distributivity equations of fuzzy implications over triangular norms and triangular conorms, the paper studies four distributivity equations of T-power implications over triangular norms and triangular conorms. Necessary and sufficient conditions for the four distributivity equations of T-power implications over triangular norms and triangular conorms are given. This paper also points out that T-power implications are different from other well-known classes of fuzzy implications, and improves finally the knowledge framework of fuzzy implications.