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 due to the fact that they were able to preserve the supremacy of its military, thanks, in part, to the development of innovative weapons, some of them made out 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 more agility, and their leaders to cover greater distances in order to supervise their troops and issue orders - warfare was essential for the Shang. On the other hand, it was also due to the fact that theirs was a very stratified government, with multiple and specialized positions that, together with the use of writing, allowed them to rule a large population and oversee a vast territory and its natural and material resources very efficiently.        

The right answer is:

A line of hereditary Shang rulers were heirs over control of northern China, and Shang troops fought wars with neighboring peoples and nomadic herdsmen from inner ancient China.

Shang kings also asserted their social supremacy by acting as high priests of society and leading the bone divination ceremonies. As the oracle bone texts reveal, the Shang kings were viewed as qualified members of society to offer sacrifices to their royal ancestors and to the god, Di.

Di, in their beliefs was responsible for the rain, wind, and thunder.

This is how Shang kings maintained their power over such vast territory and large population.

europe churches founded monasteries and universities that studied philosophy and nature.

hope this : )

the correct answer is b, "fertility rates are increasing, so populations will grow more quickly in the future."