What does it mean when there is a negative exponent in scientific notation?

There are a few reasons for negative exponents.

1) Scientific notation is a useful shorthand for expressing very large or very small quantities. In this case of very small quantities, the exponent n on the 10 is negative.

2) In algebra, you will eventually need to understand graphs of exponential functions of the form y = a * b^x, with x being any real number (so the exponent x can be negative).

3) In algebra, you will eventually need to evaluate logarithms, and an understanding of negative exponents is needed to evaluate some of the logarithms you will encounter.

4) Sometimes you will need to rewrite an expression by using a negative exponent (for example, rewriting 1 / (x^5) as x^ (-5)), in order to perform operations in calculus (such as finding derivatives or integrals).