# What Are The Laws of Indices In Math? O Level Exam Preparation Guide

This revision note aims to help your child revise the Laws of Indices and become proficient in solving the questions.

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## What Are Indices?

Index numbers (indices) in Maths is the power or exponent which is raised to a number or a variable.

Power means the number of times a base number is multiplied by itself.

For example, in 23, 3 is the index of the power of 2.

2 to the power of 3 means

23 = 2 × 2 × 2

If the index notation is an, a is known as base and n is the index or power.

an = a × a × a ….. × a (n times)

In order to do well for Secondary Math, you must be familiar with the Indices Law.

## What are the Laws of Indices?

The laws of indices provide us with simple ways to handle expressions involving powers. Here, we introduce 6 indices laws: (1) Same Bases, (2) Same Index but Different Base, (3) Power Law, (4) Negative Indices, (5) Fraction Indices, and (6) Zero Indices.

### Same Base

#### 1. Addition Law

If you multiply two variables with the same base, you need to add the powers and raise them to
that base.

Example: 23 × 26 = 29

#### 2. Subtraction Law

If you divide two variables with the same base, you need to subtract the powers and raise the new
power to the same base.

am ÷ an = am−n

Example: 27 ÷ 22 = 25

### Same index but different base

#### 3. When you multiply two variables with different bases, but with the same indices, you have to multiply its base and raise the same index to the multiplied variables.

am × bm = (a × b)m

Example: 23 × 53 = 103

### Power Law

#### 5. When a variable with some index is again raised with a different index, then you need to multiply both indices together and raise it to the same base

(am)n = amn

Example: (23)4 = 212

### Zero Indices

#### 8. If the index number is ‘0’, then the result is ‘1’ regardless of the base.

a0 = 1

Example: 20 = 1

After you are familiar with the Laws of Indices, lets explore some common Indices Math problems to help you understand how to apply them.

## Get Specialised Guidance on Indices

Indices is a crucial chapter in Secondary Maths.

It also lays the foundations of more advanced topics like Differentiation and Integration in Additional Maths.

Make sure you understand the meaning of index form, the laws of indices and the different types of Indices Math problems.

If you need more help with this chapter, feel free to check our

## Check out our exam guide on other topics here!

Circle Properties: O Level Exam Preparation Guide

All About Functions: O Level Math Exam Preparation Guide

Before you go, you might want to download this entire revision notes in PDF format to print it out, or to read it later.

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To Your Child’s Success,

Mr Tan Kok Heng
NIE Trained
Math Specialist
Jimmy Maths and Grade Solution Learning Centre

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