What is the best exercise for burning fat?

It is not so much about buring fat as it is building up your metabolism. If your body works smoothly your calories will burn away faster than you can count them.

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Anything aerobic will do the trick.  There isn't one exercise that is better than another. 

With that being said, an exercise like the elliptical machine that works the legs and the upper body at the same time may be better than the exercise bike, since it may get your heart rate higher without too much leg fatigue.

Also, remember that interval training weight weights can be a good exercise for burning fat, that is often overlooked.  Not only will weight training help you build strength & muscle mass, it will also burn plenty of calories if you go from one exercise to the next with no rest in between.

Best of luck with your program!