Final answer:
Rulers of land-based empires legitimized and consolidated power through redistribution of resources, military strength, and structured governance, while allowing cultural autonomy to stabilize their dominion.
Step-by-step explanation:
Rulers of land-based empires utilized a variety of methods to legitimize and consolidate their power. These included an economic system of redistribution where agricultural goods were collected as taxes and redistributed, the presence of military forces and sophisticated diplomatic practices such as alliances through royal marriages. The legitimacy of empires was also maintained through governance strategies such as delineating territories into administrative regions, codifying laws with publications like the Theodosian Code, and balancing power through a structured bureaucracy. These rulers also managed to maintain diverse cultures within their empires, allowing for some degree of cultural autonomy, which contributed to the stabilization of their rule.