Exponents refer to the repeated multiplication of a number, variable, or expression. The following examples show the various contexts in which exponents can be found or used:

When the exponent is positive, the exponent tells us how many times to multiply the base. From the previous examples, the exponents are expressing the multiplication as follows:

When the exponent is negative, the exponent tells us how many times to divide by the base.

The following key exponent rule can help us understand how negative exponents work:

Like the negative exponent rule, there are other exponent rules that help us better work with and simplify exponents. The following table summarizes some of these rules.

The best way to learn the exponent rules is to practice. Rather than come up with my own problems, I’ve included some practice documents involving simplifying expressions with exponents.

Practice Document 1 - with solutions

Practice Document 2 - with solutions