# Indices

## Indices

Pre-requisite:
• Know what is index notation
• Know how to do prime factorisation

Recap:
(1) Index Notation
(a) 5 x 5 x 5 = 53 is read as 5 cubed.
(b) 2 x 2 x 2 x 2 x 2 x 2 = 26 is read as 2 to the power of 6.
(c) a x a x a x … x a x a = a^n is read as a to the power of n.
(2) Prime Factorisation
(a) 12 = 22 x 3
(b) 252 = 22 x 32 x 7

Some Definitions

(a) If a number or a term is expressed in the form a^x , we say that it's in the INDEX FORM. The study of
indices is about the study of numbers in index form.
(b) If the power x is positive, we say that the term is expressed in POSITIVE INDEX FORM.
(c) If the power x is negative, we say that the term is expressed in NEGATIVE INDEX FORM.

JiTT 4: Recall the Laws of Indices learnt in Sec 1. In Sec 1, you have learnt to work with positive indices. In Sec 2, you will learn about negative indices and fractional indices, which are laws 7 and 8.

(1) Concept Mastery:
Download the summary of the laws and their proofs:

The powerpoint slides demonstrate the proofs of the laws. Though it's not necessary to show the proofs in tests/exam, it's good to know and it will help you to remember the laws:

Alternatively, you may view the video on the proofs of the laws: