Index Laws

Question 1

What is index notation for?

Answer 1

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

Question 2

Name the parts of this expression:

Answer 2

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

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 Indicies:

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. Once you move the term to the denominator, the exponent is positive.

Question 7

Expand:

Answer 7

Question 8

What is…?

Answer 8

Question 9

Rewrite with a positive exponent:

Answer 9

Note: the base stays exactly the same!

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

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

Question 20

What is…?

Answer 20

Question 21

How would you rewrite this without any index at all?

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 :)

Question 23

Express in index notation:

Answer 23

Question 24

Expand:

Answer 24

Question 25

True or false?

Answer 25

True!! Negative exponents make me sad and "bring me down", which means you put the term in the bottom of the fraction. The 3 in the y³ term is *positive*, so it stays where it is!

Question 26

True or false?

Answer 26

True!! Radicals (like a square root) can be expressed as fractional indices. Notice that we don't usually write the "2" for a square root. That's where the 2 in the bottom part of the index comes from

Question 27

True or false?

Answer 27

False! When you multiply *identical* bases together, you must **ADD** their indices.

Question 28

True or false?

Answer 28

False! You can combine identical bases ONLY when you are **multiplying** or **dividing** them

Question 29

True or false?

Answer 29

True! The y term inside the bracket has a (secret) index of 1. Both x² and y are being raised to the power of 3. This index "distributes" with the indices inside the bracket (as long as everything inside the bracket is multiplied or divided).

Question 30

True or false?

Answer 30

False! Only IDENTICAL bases can be combined, and their indices are added together. If the bases are different they CAN'T be combined.