Which factor contributed most to the growth of both the inca empire and the roman empire

they worked very hard at diplomacy, negotiating relationships with neighbors or with people who were targets for incorporation into their expanding territory; they each tried to use gifts, marital exchanges, and political alliances to further their imperial ends.  If all else fails they then undertook military conquest

"a government in which power is divided between state and national levels". federalism is a system of government in which entities such and state and province, share power with the national government.