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# Learner Guide

Index Notation

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L.O To be able to simplify expressions using the basic laws

of indices and algebra

From before we know when multiplying algebraic terms you simply remove

the multiplication and sign and place the terms together,

for example:

6 X a X p = 6ap leaving out the multiplication sign

a X b X c = abc

p X s ÷ r = ps / r

However when you have numbers involved, be aware that you have to

multiply the numbers together as well.

For example

Simplify 5b × 6s × z

 5 X b X 6 X s X z

 5 X 6 X b X s X z

 30 X b X s X z = 30bsz

Step 1: Rewrite the full expression including all the multiplication signs, it

will make things clearer.

Step 2: Place any numbers and letters next to each other so it makes it

clearer when simplifying.

Step 3: Simplify the numbers and the letters separately. Remove the

multiplication signs in the final answer.

Sometimes you will have the same letter in an expression that involves

multiplying for example: a X a or 4b X 5b . In this case not only do you have

to multiply the numbers but also the letters as well as they are like terms.

For example

Simplify 3b × 4p × 5p

 3 X p X 4 X p X 5 X p

 3 X 4 X 5 X p X p X p

 3 X 4 X 5 X p X p X p

 60p3

Step 1: Rewrite the full expression including all the multiplication signs.

Step 2: Place any numbers and letters next to each other so it makes it

clearer when simplifying.

Step 3: p X p X p  = p3 (Basic indices laws) 3 X 4 X 5 = 60

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