When there is a "little word" after a verb and the two words together have a specific definition -- "take up," "take over," "take on" -- the combination is always two words as a verb.
It needs to be looked up as a noun as it might be one word and it might be hyphenated.
...The cops will stake out the location.
...There was a stakeout at the location.
Happy punctuating!
Margie