The Rules of Exponents
Before you can get into the nitty-gritty details of polynomials, you’ve got to start somewhere simpler. Here we’re going to take a look at some basic rules of exponents that you need to know.
First, what if we multiply two values together that have exponents? Like what if we try to solve
What we have to remember is that x^4 is just x * x * x * x, and x^7 is just x * x * x * x * x * x * x. With this in mind, we can do a little simplifying and figure out a general rule:
From here, we can drop the parentheses because order doesn’t matter for multiplication because of the commutative property. That gives us
Which, by definition, is
So a general rule we can get from this is:
So for a few examples:
If we have division, a similar rule applies:
So again, for a few examples:
There is one last rule to learn, and that’s if you have a term with an exponent taken to another exponent. Here is the pattern:
Here follows a few examples of this pattern in action:
Keeping these general rules for exponents in mind will help you to work through the rest of Algebra 1 without many hangups. Learning them well means that you will breeze through all polynomial situations where you are dealing with exponents, and this will make life much easier on you.