Indices (including fractional)

Question 1

Name the parts of this expression:

Answer 1

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

Question 2

What is index notation for?

Answer 2

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

Question 3

How would you write the following in index notation?

Answer 3

Question 4

How would you rewrite the following in index notation?

Answer 4

Question 5

First Law of Indices:

Anything raised to the power of zero is…?

Answer 5

Anything raised to the power of zero is

ONE

Question 6

Second Law of Indices

A negative exponent means….

Answer 6

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.

Question 7

Expand:

Answer 7

Question 8

What is…?

Answer 8

Question 9

Rewrite with a positive exponent:

Answer 9

Note: the base DOES NOT become negative!

Question 10

3rd Law of Indices

What happens when you multiply identical bases?

Answer 10

When you multiply identical bases, their indices add together.

Question 11

Simplify:

Answer 11

Touching brackets just mean multiply, so this is

Question 12

Simplify into a single term:

Answer 12

Question 13

Write with (the secret) exponent:

Answer 13

Question 14

Rewrite as a negative exponent:

Answer 14

Question 15

4th Law of Indices

What happens when you divide identical bases?

Answer 15

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

Question 16

What is….?

Answer 16

Question 17

5th Law of Indices

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

Answer 17

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

Question 18

What is…?

Answer 18

Question 19

6th Law of Indices

What does a fractional index mean?

Answer 19

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.

Question 20

What is…?

Answer 20

Notice that in the end, I don’t write the hidden green “1” exponent…‘cause mathematicians like to hide 1s everywhere.

Question 21

What is that?!

Answer 21

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

Question 22

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

Answer 22

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