Thursday 3 rd March Index laws and notation Objective: To be able to use index notation and apply simple instances of the index laws.

Multiplication 2 3 Base number Power or index For multiplication calculations that involve indices, if the base number is the same we can simply add the indices to find our answer. 4 3 x 4 5 = = 4 8 a 3 x a 5 = a = a 8 a y x a z = a y + z

a y x a z = a Use this rule to help you simplify the following : x x x y 4 x y 3 5.m 8 x m 5 6. z 3 x z 2 x z 5 7. f 4 x 4f 7 8. r 2 x 3r 2 9.2t 3 x t x 2 x y 2 Notice that this rule will only work if the base number (or letter) is the same.

Division = = 5353 For division calculations with the same base, we can simply subtract the indices. ayay azaz = a y-z

ayay azaz = Use this rule to help you simplify the following:

Using brackets When a number raised to a power is placed inside brackets and raised to another power, we can simply multiply the indices to find our answer. (2 3 ) 2 E.g. Which means: (2 x 2 x 2) x ( 2 x 2 x 2) Which = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 (2 3 ) 2 = 2 3x2 = 2 6 (a z ) y = a z x y = a zy

Use this rule to help you simplify the following:

A few more things about indices… Any number to the power of 1 is just itself e.g. 2 1 = 2, 45 1 = 45, = 567 Any number to the power of 0 is 1. e.g. 2 0 = 1, 34 0 = 1, = 1 x 1 = xy 1 =yx 0 =1m 0 =1