I am not sure what you are seeing on the palm but it could be a surface fungus such as powdery mildew which attacks a number of different plants. I suggest you take a sample to your County Extension Office and see if they can identify the problem and if necessary prescribe an appropriate remedy. If you can also take a photo in with you or perhaps e-mail some photos to them that would help them see and better diagnose the problem. Their contact info is:
BROWARD COUNTY EXTENSION EDUCATION DIVISION
3245 College Ave, Davie, FL 33314
Phone: (954) 370-3725
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