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Negative exponents are a way of writing powers of fractions or decimals without using a fraction or decimal. You use negative exponents as a way to combine expressions with the same base, whether the different factors are in the numerator or denominator. It's a way to change division problems into multiplication problems.

Example: Instead of writing


A reciprocal of a number is the multiplicative inverse of the number. The product of a number and its reciprocal is equal to 1.


The variable x is any real number except 0, and the exponent a is any real number. And, going to the negative side,


The following examples show you how to change from positive to negative exponents, and vice versa.


If you start out with a negative exponent in the denominator, then the negative exponent in the denominator comes up to the numerator with a change in the sign to a positive exponent. For example,


Then you get,


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