Page 44 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

2 NUMBERS: INDICES
INDEX FORM
• a0 =a􏰀a􏰀a􏰀...÷a􏰀a􏰀a􏰀a􏰀...􏰀a
am = a 􏰀 a 􏰀 a ...􏰀 a 123
m factors of a = am-m
= a0
a 􏰀 a 􏰀 a
n factors of a
........􏰀 a 1
•
Where s is called the base and a is a natural number and b is called the power or index and b is a whole number.
4 factors of 7
• am􏰀an=a􏰀a􏰀a􏰀...􏰀a􏰀a􏰀a􏰀a􏰀...􏰀a
m factors of a n factors of a = a 􏰀 a 􏰀 a 􏰀 ....􏰀 a
(m + n) factors of a . .. a m 􏰀 a n = a m + n
So 53 􏰀 54 = 5 􏰀 5 􏰀 5 􏰀 5 􏰀 5 􏰀 5 􏰀 5 3 factors of 5 4 factors of 5
= 5 􏰀 5 􏰀 5 􏰀 .......􏰀 5
= 53+4 (3+4) factors of 5 53 􏰀 54 = 57
• am􏰁an=a􏰀a􏰀a􏰀...􏰀a􏰁a􏰀a􏰀a􏰀...􏰀a m factors of a n factors of a
= a 􏰀 a 􏰀 a 􏰀 ....􏰀 a (m 􏰂 n) factors of a
. .. a m 􏰁 a n = a m - n
So 75 ÷ 73 = 7 􏰀 7 􏰀 7 􏰀 7 􏰀 7 ÷ 7 􏰀 7 􏰀 7
0 1
anda =a􏰀a􏰀a􏰀......􏰀a
So 74 = 7 􏰀 7 􏰀 7 􏰀 7 123
. .. a 0
=1
= 1
m factors of a
1 1
1
1 1
1
(cancelling)
NEGATIVE INDEX
123
EXAMPLE 1
5 factors of 7
= 7 􏰀 7 􏰀 7 􏰀 ....7
(5 – 3) factors of 7 = 7(5-3)
3 factors of 7
. ..
7 5 ÷ 7 3
= 7 2
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