Index Laws

1
Index Laws
Objectives
Prior knowledge
Understand
Use Index Laws for positive and negative powers
2
Index Laws
Using the index laws to simplify a3 a4
a34 a7
Understanding that we add the index numbers we
can deduce the meaning of
100½ 100½
By adding the index numbers
100½½ 1001 100
Therefore 100½ is a number, that, when multiplied
by itself is 100.
We know that
v100 v100 100
Therefore
100½ v100
The general rule is
3
Index Laws
Understanding that we add the index numbers we
can deduce the meaning of
By adding the index numbers
3v100 3 v100 3 v100 100
Therefore
The rule is
The general rule is
4
Index Laws
1
2
5
2
2
9
3
8
5
Index Laws
More complex fractional index laws together
(73) (73)
(73)2 means
76
733
(4½)3 means
4½ 4½ 4½
Therefore when we see
We know it means (4½)3
6
Index Laws
9
25
8
8
729
81
64
32
7
Index Laws
8
25
100
1000