The correct explanation for how the Aztec used local rulers to help them rule politically is D. local rulers maintained their local rule but had to provide tribute.
The Aztec Empire integrated various city-states and regions through a political system that allowed local rulers to maintain a degree of autonomy and control over their own people. However, these local rulers were required to pay tribute to the Aztec Empire, which included goods and resources. This approach allowed the Aztecs to exert influence and maintain control over vast territories without having to directly govern every local area, thus facilitating a more efficient administration of the empire while also respecting local customs and leadership structures.