TOPIC 1 : INDICES

Introduction Of Indices : 

A power, or an index, is used to write a product of numbers very compactly. The plural of index is indices. 

Law Of Indices : To manipulate expressions, and these laws only apply to expressions with the same base, for example,  3⁴ and 3² can be manipulated using the Law of Indices, but we cannot use the Law of Indices to manipulate the expressions 3⁵ and 5⁷ as their base differs.

  FIRST LAW:    

When expressions with the same base are multiplied, the indices are added. 

Example -

Simplify : (note: 5 = 5¹)

SECOND LAW:       

Any number, except 0, whose index is 0 is always equal to 1, regardless of the value of the base.

Example -

Simplify 2⁰

                                  THIRD LAW:      

Simplify 2^-2:

                                      FOURTH LAW:   

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

Example -

Simplify

:

                                       FIFTH LAW:  

To raise an expression to the nth index, copy the base and multiply the indices.

Example - 

Simplify (y²)⁶:

                                        SIXTH LAW:  

Example - 

Simplify 125^2/3:

QUESTIONS⏩⏩

1. Without using a calculator work out the value of :

       a) 42                   e)1 3 2

       b) 53                   f) 2 5 3

       c) 25 

       d) 1 2 2