Why would the word empire apply to Hammurabi's rule of Babylon?

The term "empire" applies to Hammurabi's rule of Babylon because he expanded his territory through military conquests and diplomatic alliances, uniting various city-states under Babylonian control. His establishment of a centralized government and the infamous Code of Hammurabi created a cohesive legal framework that helped maintain order across the diverse regions he governed. This combination of territorial expansion, centralized authority, and legal uniformity exemplifies the characteristics of an empire.