Final answer:
The Dutch East India Company established control of the Dutch East Indies by setting up trading posts and colonies, amassing wealth from the spice trade. They also established a presence in the Caribbean, controlling trade and practicing piracy.
Step-by-step explanation:
The Dutch East India Company (DEIC) established control of the Dutch East Indies by establishing trading posts and colonies in modern-day Indonesia and South Africa. These ports allowed the Dutch to amass wealth from the spice trade, which was a lucrative industry at the time. The DEIC operated as a quasi-governmental entity and had quasi-governmental powers, making it more than just a trading company.
Additionally, the Dutch established their presence in the Caribbean through the Dutch West Indies Company. They were successful in controlling both legitimate and black market Caribbean trade, becoming a powerful shipping empire. They also practiced piracy and captured a Spanish treasure fleet, which weakened Spanish control in the region.