Indices and Surds

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 = 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

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.

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

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:

Surds