Final answer:
The Spanish maintained the stability of their colonial empire by collaborating and rewarding Creole elites.
Step-by-step explanation:
To maintain the stability of the colonial empire, the Spanish collaborated and rewarded Creole elites to keep them in the Spanish fold. This strategy involved granting privileges and positions of power to the Creole elites, who were individuals of Spanish descent but born in the colonies. By aligning the interests of the Creole elites with those of the Spanish empire, Spain aimed to maintain control and prevent unrest or rebellion.
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