Name the parts of this expression:

The term being raised to a power is called the "base" and the power is the "index" or exponent.

What is index notation for?

To write and manipulate long algebraic expressions, very big or very small numbers easily.

How would you write the following in index notation?

How would you rewrite the following in index notation?

**First Law of Indices:**

** Anything** raised to the power of zero is...?

** Anything** raised to the power of zero is

**ONE**

__Second Law of Indices__

A negative exponent means....

Negative exponents make you sad and "bring you down", which means you put the term in the bottom of a fraction. The negative sign morphs into the fraction symbol and the base ("a") and positive of the exponent ("2") hang out in the bottom. If there's nothing to go on top, it's just a 1.

Expand:

What is...?

Rewrite with a positive exponent:

*Note: the base DOES NOT become negative!*

**3rd Law of Indices**

What happens when you **multiply** *identical* bases?

When you **multiply** *identical* bases, their indices add together.

Simplify:

Touching brackets just mean multiply, so this is

Simplify into a single term:

Write with (the secret) exponent:

Rewrite as a negative exponent:

**4th Law of Indices**

What happens when you **divide** *identical* bases?

When you **divide** *identical* bases, the indices subtract: exponent from the top - exponent from the bottom:

What is....?

**5th Law of Indices**

What happens when an index is raised to the power of another index?

When an index is raised to the power of another index, they multiply together

What is...?

**6th Law of Indices**

What does a fractional index mean?

A **fractional index** is a RADICAL way of expressing a **RADICAL**

That green m can be under the radical or hanging waaaay outside. It doesn't matter. You choose whichever way you like better.

What is...?

Notice that in the end, I don't write the hidden green "1" exponent...'cause mathematicians like to hide 1s everywhere.

What is that?!

It is a bring-me-down-RADICAL combo!

How do you deal with a negative index that's ALREADY in the bottom part of a fraction?

Negative exponents make me flip out! Flip the term to the other side of the fraction to make the index positive :)