Final answer:
King Louis XIV; French was the monarch who sent René-Robert Cavelier de La Salle to explore, while Pedro Cabral was the first explorer to claim Brazil for the throne of Portugal. Both men played significant roles in the historical narrative of European exploration and colonialism.
Step-by-step explanation:
The monarch who sent René-Robert Cavelier de La Salle to explore was King Louis XIV; French. This makes the correct answer (b) King Louis XIV; French. King Louis XIV is renowned for epitomizing the divine-right monarchy in France and for his role in the establishment of a powerful and centralized state. He was keen on expanding France's territorial claims, which led to explorations into North America.
Regarding the first explorer to reach Brazil and claim it for the throne of Portugal, the correct answer is Pedro Cabral. This explorer is credited with the discovery of Brazil in 1500, which he claimed for Portugal. This event was part of the wider European age of exploration and the subsequent imperialistic endeavors that had a significant impact on world history.