  Monogamy relations characterize the distributions of quantum entanglement in
multipartite systems. In this work, we present some tighter monogamy relations
in terms of the power of the Tsallis-q and R\'{e}nyi-$\alpha$ entanglement in
multipartite systems. We show that these new monogamy relations of multipartite
entanglement with tighter lower bounds than the existing ones. Furthermore,
three examples are given to illustrate the tightness.
