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,