Final answer:
European engagement in the Indian Ocean was driven by trade and new markets, while in the Americas, it focused on economic exploitation and cultural dominance.
Step-by-step explanation:
European engagement in the Indian Ocean was driven by the pursuit of trade and new markets, while in the Americas, it was influenced by the search for precious metals and agricultural products. In the Indian Ocean trade networks, European powers sought to establish cultural dominance and control over trade routes. In contrast, in the Americas trade networks, European interaction primarily focused on economic exploitation, such as the extraction of raw materials and the enslavement of indigenous populations.