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

Laws of Indices Module C1 Edexcel OCR MEI/OCR Module C2 AQA "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"

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

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

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

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

Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer

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

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

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

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

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

Laws of Indices 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 numbersand

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

Laws of Indices SUMMARY The following are the laws of indices:

Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer

Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer or fraction

Laws of Indices

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Laws of Indices SUMMARY The following are the laws of indices:

Laws of Indices Examples

Laws of Indices