# Common Core Standards: Math

#### The Standards

# Grade 8

### Expressions and Equations 8.EE.A.1

**1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^{2} × 3^{-5} = 3^{-3} = 1/3^{3} = 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,*a*^{3}·*a*^{5}=*a*^{8}because 3 + 5 = 8. - If multiplication means adding exponents, then
**dividing**means**subtracting**exponents. That means*n*^{7}÷*n*^{3}=*n*^{4}because 7 – 3 = 4. - When there's an exponent on an exponent, the exponents are
**multiplied**. For example, (*x*^{5})^{2}=*x*^{10}because 5 · 2 = 10. - A
**negative**exponent means we take the**reciprocal**of the base. So 2^{-2}= ½^{2}= ¼. **Anything**raised to the 0 power is 1. So*x*^{0}= 1 and 57^{0}= 1 and 0^{0}= 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.

#### Drills

### Aligned Resources

- Properties of Exponents - Math Shack
- Power to a Power - Math Shack
- Evaluating Algebraic Expressions - Math Shack
- Properties of Integer Exponents - Math Shack
- More Practice with Integer Exponents - Math Shack
- Negative Exponents - Math Shack
- Evaluating Rational Expressions - Math Shack