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 = an 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 ax , 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. 1. Concept Mastery - recall the 8 laws of Indices Download the summary of the laws of indices:

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View the powerpoint slides to recap the laws and the proofs of the laws. Although you are not required to demonstrate the proofs, it is good to know and it's relatively easy to understand.

To solve equations involving indices (usually called exponential equations) these are some considerations to help simplify the process: - Try to change the base of both sides of the equation to the same base. - Usually a prime number base is preferred. - Compare the index of both sides to the equation. - At other times, it may be necessary to change them to the same index and compare their base instead.

View these slides to see examples of how to solve exponential equations:

## Indices

Pre-requisite:

index notationprime factorisationRecap:

(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 = an 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

ax, we say that it's in theINDEX FORM.The study ofindices 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.1. Concept Mastery - recall the 8 laws of IndicesDownloadthe summary of the laws of indices:File Not FoundView the powerpoint slides to recap the laws and the proofs of the laws. Although you are not required to demonstrate the proofs, it is good to know and it's relatively easy to understand.

If you prefer to learn via watching a video, here is one explaining the laws:

[URL: http://www.youtube.com/watch?v=wCM77K_DWuQ]

To see how Indices can be simplified by applying the laws, view these slides:

To solve equations involving indices(usually called exponential equations) these are some considerations to help simplify the process:- Try to change the base of both sides of the equation to the same base.

- Usually a prime number base is preferred.

- Compare the index of both sides to the equation.

- At other times, it may be necessary to change them to the same index and compare their base instead.

View these slides to see examples of how to solve exponential equations:

SurdsVideo showing multiplication of surds

URL:http://www.youtube.com/watch?v=FBp8325umpU

Slides on Surds: