a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression
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When dividing numbers with exponents, subtract the bottom exponent from the top exponent.
It wasn't necessary to 'create' any rules. They follow logically from the definition of exponents.
property of negative exponents
power in a math term is when you multiply the exponents
It certainly has a meaning. It is only meaningless if you consider powers as repeated multiplication; but the "extended" definition, for negative and fractional exponents, makes a lot of sense, and it is regularly used in math and science.