Final answer:
The Manchu rulers gained the respect of their conquered peoples through military conquest, adopting the culture and customs of the conquered people, implementing a policy of religious tolerance, and establishing a stable and efficient government.
Step-by-step explanation:
The Manchu rulers gained the respect of their conquered peoples through a combination of military conquest and adopting the culture and customs of the conquered people. They implemented a policy of religious tolerance and incorporated elements of the foreign culture into the practices of the Chinese state. The Manchu rulers also established a stable and efficient government, which helped to maintain their superior positions and demand loyalty from the Chinese.