Unit 2

EXPONENTS

The exponent of a number says how many times to use the number in a 

multiplication.

In 8² the "2" says to use 8 twice in a multiplication,
so 8² = 8 × 8 = 64

Exponents are also called Powers or Indices.

• In words: 8² could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"
  

Some more examples:

Example: 5³ = 5 × 5 × 5 = 125

• In words: 5³ could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"
  

Example: 2⁴ = 2 × 2 × 2 × 2 = 16

• In words: 2⁴ could be called "2 to the fourth power" or simply "2 to the 4th"
  
  LAWS OF EXPONENTS
  
  
  
  

SQUARE ROOTS
A square root of a number is a value that can be multiplied by itself to give the original number.
A square root of 9 is 3, because when 3 is multiplied by itself you get 9.
It is like asking:

What can I multiply by itself to get this?

To help you remember think of the root of a tree:

"I know the tree, but what is the root that produced it?"

In this case the tree is "9", and the root is "3".

The Square Root Symbol

This is the special symbol that means "square root", it is sort of like a tick, and actually started hundreds of years ago as a dot with a flick upwards.

It is called the radical, and always makes math look important!

You can use it like this:

you would say "square root of 9 equals 3"

THE CUBE ROOT

 The cube root of a number is a special value that when cubed gives the original number.

The cube root of 27 is 3, because when 3 is cubed you get 27.

The Cube Root Symbol

This is the special symbol that means "cube root", it is the "radical" symbol (used for square roots) with a little three to mean cube root.

You can use it like this: (you would say "the cube root of 27 equals 3")

Summary:
   Let n be the index of the radical

• If n=2 then we have a square root
• If n=3 then we have a cube root
• If n=4 then we have a fourth root
• If n=5 then we have a fifth root
• ... 

PRACTICE WITH THE FOLLOWING EXCERCISES: