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Having a relaxed but firm grip on the racket is very important in squash. Your grip should be light enough to be able to feel the ball but strong enough to prevent the racket moving in your hand when you hit the ball, particularly if you have hit it off centre. Strong forearm muscles are key. You can get aids that improve your grip strength but here is an racket and ball exercise you can do on court.
Bounce the ball on the floor with the forehand side of the racket. Try to use your wrist and forearm rather than the whole arm. Don't go mad with this as you do not want to get any repetition injuries: you will be able to feel when your wrist and forearm is tightening up, so stop, have a short rest to relax the muscles and repeat.
Experiment with a backhand bounce too, it is much harder to do! It also has the added benefit of warming the ball up!