Introduction to Exponents - Concept
Since we often see exponents throughout all math courses, it is important to understand the rules of exponents. We need to understand how to distribute, add, multiply and divide exponents in order to simplify expressions or manipulate equations that have exponents. The rules of exponents, like those involving multiplication of terms, are important to learn and will be used throughout Algebra I and II and Calculus.
There's a whole lot to learn about exponents, you probably already know quite a bit. When you start getting further and further into your study of exponents you'll see lots of properties and little shortcuts that a lot of students use to help them. However you don't have to memorize anything and in fact I suggest that you don't memorize anything. You just want to be sure you're comfortable with a few basic properties of exponents. An exponent tells how many times a number or a base is multiplied by itself. You know what I'm talking about, like if I have 4 to the first power, 4 is the base, 1 is the exponent. That means 4 times itself 1 time. You could also write 4 squared which means 4 times itself twice or 4 times 4. 4 to the third power would be 4 times 4 times 4 times 4 again, you could think of that as 16 times 4 or jump right to how that is equal to 64 et cetera. this goes on and on. You could write 4 to the fourth that's 4 times 4, times 4, times 4, times 4 blah blah.
That's one thing to keep in mind, one thing you really have to be careful though with you guys is exponents. When it comes to exponents and negative signs especially ait gets tricky, here's what I mean, if I have negative 4 as the base and I wanted it to be squared I would have to write negative 4 in parenthesis squared. That's different than this, this means with no parenthesis this means 4 squared then negativised. Please write this down somewhere where you'll see it over and over again, and so you can get this into your brain. It's a tiny little mistake that can really throw off all of your work with exponents.
One other thing I want to show that's similar to this is the difference between 3x in parenthesis squared in which case 3x is the base so when I square it I'll have 3 squared times x squared or 9x squared. That's totally different from if I write 3x squared, 3x squared is just 3 times x times itself. be careful there's all kinds of little tricks like these that you're going to run into with exponents that you want to make sure you keep straight in your head.
If you don't remember anything else then you don't have to memorize anything going into exponents as long as you can remember the difference between this kind of notation and that kind of notation. Same thing here difference between 3x squared versus 3x squared. Exponents can be tricky guys but if you can just remember to try to write things out and be careful with your parenthesis you'll have a lot of success.