Quantum resource theories offer formal frameworks for quantification and manipulation of intrinsic resources associated in quantum systems. Each resource, such as quantum entanglement, coherence, contextuality and many others, has attracted considerable interest encompassing the characterization, quantification, and its operational application. Despite the fundamental importance of quantum resource, the development of a unified framework of resource theories has been initiated only recently, especially in the framework of additive quantum resources. Monogamy is a fundamental property of many entanglement measures, and a unified view to monogamy inequalities of bipartite entanglement in multi-party quantum systems has recently been established. By investigating the monogamy property of the additive quantum resource, general monogamy inequalities given by the α th power of additive quantum resource measures are presented: any additive resource measure satisfy the polynomial relation for α ≥ 1 and obey monogamy inequalities for α ≤ 0. However, the relation is not clear for 0 < α < 1. These relations add a fundamental item to the list of common properties based on the tensor product structure for the general quantum resources.