How did shang kings retain their power over such a large population and vast territory?

I would argue that, on the one hand, it was because of the development of innovative weapons, some of them made of bronze, such as bronze-tipped halberds and spears, the compound bow, and the horse-drawn chariot, which allowed soldiers to move faster and with greater agility, and their leaders to cover greater distances in order to supervise their troops and issue orders - warfare was a more efficient and effective method of conflict resolution. However, they were able to rule a big population and manage a wide region and its natural and material resources effectively thanks to their government's highly stratified structure, which included numerous and specialized roles.

"budgeting is not just for the people who do have enough money. it is for everyone who wants to ensure that their money is enough."