x^a / x^b = x^(a-b)and
x^a * x^b = x^(a+b)
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It wasn't necessary to 'create' any rules. They follow logically from the definition of exponents.
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1. Find the value of the exponent. 2. Multiply or divide normally.
When multiplying numbers with exponents, you add the exponents.
When dividing numbers (or variables) subtract the exponents. Remember, an exponent indicates a kind of multiplication, it is the number of times that a number is multiplied by itself. If you are dividing by that same number, then clearly you are multiplying it by itself a fewer number of times. Division is the inverse function of multiplication.