When simplifying an expression that includes exponents there are exponents laws that one could use to answer the question easier. The laws of exponents can be thought of just “tricks” or shortcuts that help us work with exponents in equations. Some of these laws for exponents are the Power Law, Multiplication Law, and Division Law. However, we are going to focus on just the division law.

The first thing to do when using the division law is to identify the same bases with exponents. If the bases are not the same, you can’t use the division law and won’t be able to simplify it any more. Next, you will subtract the exponents leaving you with one number with one exponent. To divide exponents (or powers) with the same base, subtract the exponents. The coefficients (if any) won’t be affected by the division law. As division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

My example:

If when you are subtracting the exponents and the result is a negative exponent then you will use the Negative law to further simplify the expression.