What's the best way to handle early traders

I've played some people at 10 minute chess who try to trade pieces off as fast as possible to make the board simple enough that even they can understand it, and then they have about a 50-50 chance of winning :-)  How do I handle that? By learning how to play chess better? Or is there a trick?

It shouldn't bother you that pieces are exchanged; chess is still chess even in endgame phase. Capablanca was at his best in simple positions.

In any case, you should welcome exchanges of your bad pieces for your opponent's good ones. Don't worry if he trades his good knight for your bad bishop or if he takes a lot of moves with a developed piece only to exchange one of your less devloped piece. Anyway, it's hard to talk in general about this because it is the concrete position that decides whether an exhange is good or bad. 

What openings do you play as White and Black? Some openings encourage more "trading down" than others but I don't know what to  suggest without knowing what you play or prefer to play. BTW mindless trading down can backfire on these people, there are often various factors involved on what to trade and when. For instance, if you have a "bad" bishop hemmed in by your pawns and/or your opponents trading it off for a Kt is usually good for you. On the other hand if the board is open its usually better to trade off your Kts for your opponents bishops. If you're a pawn up trade pieces (simplify) If you're a pawn down trade pawns not pieces (complicate). This isn't even scratching the surface, I'm just trying to give you a very brief overview here. 

Start studying endgames, because it sounds like your opponents are trying real hard to reach an endgame, whether or not they realize it. I can almost promise if you spend even a few hours on memorizing basic endgame principles you'll have a big advantage over many opponents. Focus on basic K+P endings first, next work on R+P endings which are by far and away the most common type of endgame.

http://www.chess.com/blog/NimzoRoy/endgame-faqs?_domain=old_blog_host&_parent=old_frontend_blog_view

http://www.chess.com/blog/NimzoRoy/endgame-books?_domain=old_blog_host&_parent=old_frontend_blog_view

To improve at chess you should in the first instance study the endgame.  -  CAPABLANCA

In order to improve your game, you must study the endgame before everything else. For whereas the endings can be studied and mastered by themselves, the openings and middle game must be studied in relation to the end game.  CAPABLANCA

The amount of points that can be gained (and saved) by correct endgame play is enormous, yet often underestimated by youngsters and amateurs.  -  EDMAR MEDNIS 

Try to get the bishop pair, try to double pawns during exchange, try to get rook on the open file. Play d4 positional openings.

I'm always trying to get my rooks off.

I've heard of exchanging queens but she won't go for that.