Indices

What are Indices?
Indices are a useful way of more simply expressing large numbers. They also present us with many useful properties for manipulating them using what are called the Law of Indices. 

Six rules of the Law of Indices

Rule 1:

An Example:
Simplify 2⁰:    

Rule 2:

 An Example

Simplify 2^-2:

 

Rule 3:

An Example:

Simplify : (note: 5 = 5¹)

Rule 4:

To divide expressions with the same base, copy the base and subtract the indices.

An Example:

Simplify

:

Rule 5:

To raise an expression to the nth index, copy the base and multiply the indices.
An Example:
Simplify (y²)⁶:

 Rule 6:

An Example :

Simplify 125^2/3:

 Here's another video of Indices Formula:

Most if you will be able to simplify indices, but not all will get full marks because you may make mistakes while cancelling.

EXERCISE

What is the value of 6³ ?

A. 18

B. 216

C.729

D.1,296

What is the value of 2² - 2^-2 ?

A. 0

B. 3.75

C. 4

D. 4.25

 

What is the value of 5² + 6² ? 

A. 22

B. 51

C. 61

D. 121