Final answer:
Prospero keeps control over Ariel and Caliban through a combination of magic spells and bargaining.
Step-by-step explanation:
Prospero keeps control over Ariel and Caliban through a combination of magic spells and bargaining.
Regarding Ariel, Prospero initially freed him from a tree where he was imprisoned by the witch Sycorax. In return, Ariel agreed to serve Prospero and obey his commands. Prospero uses his magic spells to control and manipulate Ariel, threatening to imprison him again if he does not follow orders.
As for Caliban, Prospero exerted control over him by bargaining with him. Caliban desired freedom, so Prospero promised to grant him his wish if Caliban followed his instructions and assisted him in carrying out his plans.