Austronauts crash and see the kids acting like apes. They then say "Oh my God! We've landed thousands of years into the future and apes have taken over!" "You blew it up! Didn't you!" which is what happens in this film. "You blew it up!" is a quote from the film.
When acting like an ape, Stan picks up a bone and the music cue from this movie plays.
The boys act primitive around Bebe and her boobs, and Stan begins to refer breats as "Atar", in Quest for Fire, "Atar" means fire.
Cartman acts out this film with toys, he quotes the famous "It puts the lotion on it's skin" lines.