Final answer:
The Portuguese challenged European dominance in the Indian Ocean by monopolizing the spice trade, asserting naval power, demanding permits for trade, and forming strategic alliances. They also faced opposition from local and external forces forming the League of the Indies.
Step-by-step explanation:
The Portuguese challenged the European presence in the Indian Ocean by seeking to monopolize the lucrative spice trade and asserting their dominance through naval power. After Bartholomew Diaz rounded the Cape of Good Hope and Vasco da Gama reached India, Portugal rapidly established trading routes and demanded that all ships in the region carry a cartaz, a special permit indicating Portuguese authorization. Their quest for control also included military confrontations, as when da Gama bombarded Calicut for defying his demands, and strategic alliances meant to divide and conquer local rulers.
By conquering strategic points like the Strait of Malacca, the Portuguese effectively broke the Arab dominance in the spice trade and redirected these rich trade flows to Europe, benefiting the Portuguese crown. Their naval expeditions and the expansion of trade paved the way for European global exploration and colonial dominance. However, their monopoly in the region triggered alliances against them, including the formation of the League of the Indies, although the lack of Ottoman support due to conflicts elsewhere limited the effectiveness of this resistance.