Final answer:
The Spanish and Portuguese managed their new worlds by establishing colonial governments, imposing their culture and language, and exploiting indigenous resources.
Step-by-step explanation:
The Spanish and Portuguese managed their new worlds by establishing colonial governments, imposing their culture and language, and exploiting indigenous resources. One example of this is the encomienda system, in which indigenous people were used for forced labor on Spanish and Portuguese plantations and mines. Another example is the imposition of Catholicism as the dominant religion in the colonies. The Spanish and Portuguese also established strict trade regulations through mercantilism, ensuring that all profits from colonial trade went back to the mother country.