Common Core Standards: Math
1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.
We're guessing your students aren't huge fans of rules. They're in eighth grade. They're teenagers, and teenagers are automatically supposed to rebel against any rules. Just look at James Dean, the Fonz, and even Carly and Sam from iCarly. We get it.
The thing is, these rules are cool. They'll help your students deal with those pesky little numbers called exponents. That will help them get a high school diploma, which will help them get into college, which will help land them a great job, which will lead to them being cooler than Fonzie on a motorcycle.
But before they can do that, they should know how to handle exponents and it all starts with the List of Rules. Sounds official, doesn't it?
- When multiplying terms with the same base, the exponents are added together. For instance, a3 · a5 = a8 because 3 + 5 = 8.
- If multiplication means adding exponents, then dividing means subtracting exponents. That means n7 ÷ n3 = n4 because 7 – 3 = 4.
- When there's an exponent on an exponent, the exponents are multiplied. For example, (x5)2 = x10 because 5 · 2 = 10.
- A negative exponent means we take the reciprocal of the base. So 2-2 = ½2 = ¼.
- Anything raised to the 0 power is 1. So x0 = 1 and 570 = 1 and 00 = 1. This one fools a lot of wannabe cool people.
Students should also know that these rules are meant to simplify their lives, not complicate them. After all, being cool is a way of life—and the last thing we want to do is cramp their style.