The book refers to china and the byzantine and abbasid empires as "political and economic anchor[s] of the postclassical world." what does this phrase mean? what did all three of the powers have in common? how did those factors contribute to their political and economic effectiveness?

Yes, these three empires founded the thought of the post-classical world economy and its freshness is based on three basic factors, including the benefit of the individualAnd the common political thing is that the imperial decision is made in the center and imposed on the parties, while hegemony takes the form of a joint decision with greater influence of the dominant power.

Economically some areas enjoy managing their resources but the center always determines what type of tax will pay me as a barter to manage daily mantras

Well, talking about trade they were the greatest in the world. They used to have a lot of access to water for trade and each one had a long coastline. They traded successfully because of the water that had each empire and able to grow even more due its surplus of goods from the trade.

to fight against injustice and class division

that’s true, tatiana prouskouriakoff established that the inscriptions were primarily historical.   they recorded events in the lives of mayan rulers and their families.