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Extermination was the goal of the Daleks, who sought to kill all other lifeforms in existence. (TV: Genesis of the Daleks) Though used synonymously with pest control or genocide, (TV: Doomsday, Evolution of the Daleks) the execution of a single lifeform could be referred to as extermination. (TV: The Parting of the Ways) The Daleks' first and foremost instrument of extermination was their personal gunstick located on their weapons platform. Before firing a fatal blast, the Daleks would typically and loudly exclaim "Exterminate!" (TV: Genesis of the Daleks)
A most prolific subject of the Daleks' hatred was the Time Lord known as the Doctor. As such, most Daleks sought to kill the Doctor on sight. (TV: Remembrance of the Daleks, Dalek, Evolution of the Daleks)
Similarily, the Cybermen of Pete's World, whom the Daleks engaged in the Battle of Canary Wharf, (TV: Doomsday) sought to "delete" all those they deemed incompatible for the upgrade to cyber-form. (TV: Rise of the Cybermen/The Age of Steel) Cybermen of N-Space used eradication. (TV: Silver Nemesis)
Eve, a survivor of the Last Great Time War, recalled that so many of her people were "exterminated" when her home planet was attacked during the conflict between the Daleks and the Time Lords. (TV: Sarah Jane's Alien Files episode 2, The Mad Woman in the Attic)
During the 21st century Dalek invasion, the gunstick of one Dalek successfully inflicted a mortal wound against the Tenth Doctor, who was forced to regenerate, but used his severed hand to keep himself from changing form. (TV: The Stolen Earth/Journey's End)
On Lakertya, Beyus warned Melanie Bush against antagonising the Rani, claiming that she had only to press a button for every Lakertyan to be exterminated. Mel quipped that she herself could nominate a few candidates for extermination. (TV: Time and the Rani)