I’ve got the base version of catan and was going to buy the explorers and pirates expansion and the relevant extension for extra players. Do I also need to buy the extension of the base game?
I'm not sure about the American editions (by Mayfair IIRC?), but for the German editions by Kosmos the answer is yes. The base game as well as the expansions had the material for 3 and 4 players, and all expansions and the base game each had an individual extension for 5th and 6th player.
The expansions and their 5/6-extensions only contain the additional material, you are supposed to use the roads, settlements and cities from base game, so you need the base game's 5/6-extension, too.