Negative exponents represent the reciprocal of a number raised to a positive exponent. For example, a^-n is equal to \frac1a^n . This means that instead of multiplying the base a by itself n times, you divide 1 by a multiplied by itself n times. Negative exponents are useful in simplifying expressions and solving equations. They help in expressing very small numbers in a more manageable form. For instance, 10^-3 equals \frac11000 , which is easier to work with in calculations involving scientific notation or engineering.