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# What is the quotient of powers?

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The quotient of powers is a mathematical rule for evaluating a division problem in which both the numerator and the denominator are taken to different powers. It states that the exponent in the denominator is subtracted from the exponent in the numerator.

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For example, the quotient of powers rule can be used to express the equation x^a/(x^b) as x^(a - b). The rule works by cancelling out equal factors in the numerator and the denominator until either the top or bottom power is equal to 1. The quotient of powers rule is similar to the product of powers rule, in which the exponents are added instead of subtracted.

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