“Teach A Level Maths” Vol. 1: AS Core Modules 19: Laws of Indices © Christine Crisp

Module C1 Module C2 Edexcel AQA MEI/OCR OCR "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

Multiplying with Indices e.g.1 e.g.2 Generalizing this, we get:

Multiplying with Indices If m and n are not integers, a must be positive e.g.3

Dividing with Indices e.g. Cancel Generalizing this, we get:

Powers of Powers e.g. by rule (1)

Exercises Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

A Special Case e.g. Simplify Using rule (3) Also,

A Special Case e.g. Simplify Using rule (2) Also, So, Generalizing this, we get:

Another Special Case e.g. Simplify Using rule (3) Also,

Another Special Case e.g. Simplify Using rule (3) Also, So,

Another Special Case Generalizing this, we get: e.g. 1 e.g. 2

Rational Numbers A rational number is one that can be written as where p and q are integers and e.g. and are rational numbers are not rational numbers and

p is the power Rational Numbers The definition of a rational index is that e.g.1 p is the power q is the root e.g.2 e.g.3

SUMMARY The following are the laws of indices:

Exercises Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

Exercises Without using a calculator, use the laws of indices to express each of the following as an integer or fraction 4. 5. 6.

The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

SUMMARY The following are the laws of indices:

1. 2. 3. Examples

4. 5. 6.