Final answer:
Events in Europe, specifically the actions of France and the Netherlands, weakened the authority of the Spaniards and Portuguese in their Latin American empires.
Step-by-step explanation:
The authority of the Spaniards and Portuguese in their Latin American empires was weakened by events in Europe. France and the Netherlands played a significant role in undermining their power. The French attempted to establish a colony in Florida to disrupt Spanish shipping lanes, while the Dutch engaged in piracy to weaken the Spanish economically. The Dutch also conquered parts of Brazil, challenging Portuguese control. These actions by France and the Netherlands politically and economically weakened the authority of the Spaniards and Portuguese in their Latin American empires.