To what extent is Shakespeare's The Tempest a play about authority and power?

From the Master's opening commands to the Boatswain to "speak to the mariners" to Prospero's final mitigated imperative in the Epilogue asking the audience to "set [him] free" through applause, The Tempest presents three individual, but inevitably interwoven plot lines that all have their foundation in systems of authority and power. The scenes of the King's company are characterised by attempts to gain power through political intrigue. Antonio and Alonso exiled Prospero (explained to the reader by Prospero at the start of the play) to ensure their authority within Naples was paramount and unchallenged, with Antonio then plotting with Sebastian to overthrow Alonso to gain the same for himself. Likewise, Prospero's initial conquering of the island and its 'master' Caliban was in order to fulfil the need to control and establish hierarchical power with his own authority at the head. Caliban, enslaved, is rendered unable to fathom a life without servitude. Even when he is supposedly freed of Prospero's control by Stephano and Trinculo, he can only chant "Ban, 'Ban, Ca-caliban/ Has a new master. Get a new man./ Freedom, high-day, high-day, freedom [...]". His idea of freedom reinstates servitude, evidencing Prospero's complete authority over and alteration of Caliban. Even Miranda and Ferdinand's relationship, intended to be a light-hearted respite from the political wranglings of the other plots, is a method of ensuring political alliance and stability for Prospero. In fact, alongside being a medium to obtain control, Ferdinand displays awareness of power structures in marital relationships. He uses the semantic field of submission in his conversations with Prospero and even further demonstrates his subservience towards Miranda, his "mistress [to] serve"; this deference is later revealed to be only a method of courtship as he tells his father of their marriage, declaring "she's mine./I chose her". Ultimately, Prospero seems to be at the root of these power systems. He causes the tempest that brought the king's company to the island, uses his servant Ariel to manipulate the king's company to his will as well as Prince Ferdinand whom he marries to his daughter. It is through these manoeuvrings, by way of both magical power and political manipulations, that he is able to reestablish his authority within the systems of control in Naples.