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
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.
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.
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:
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
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.
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 :)