Algebra I For Dummies
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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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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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