1. Index Laws
Objectives:
B Grade Use Index Laws for positive and negative powers

2. Index Laws
Use the index laws to calculate:
x x 4 =
x(2-4)
= x-2
What does this mean?
x × x
x × x × x × x
In full this looks like:
x × x
x × x × x × x 1 x2
Simplify =
x-2 = 1 x2 So
x-y = 1 xy
This result can be generalised for all negative indices

3. Index Laws
Other examples:
5-2 = 1 52
3-1 = 1 3
5x-2 = 5 x2

4. 1. Write these in fraction form a) 5-3 b) 10-5 c) 8-2 d) x-m
Now do these:
1. Write these in fraction form
a) b) c) 8-2 d) x-m
2. Write these in negative index form
a) b) c) d)
3. Change each fraction to index form
a) b) c) d)
4. Find the value of each of the following
a) Where x = 5
i) x2 ii) x-3 iii) 4x-1
5. Change the following to index form 2n
i) 16 ii) iii) iv) -8
Change the following to index form 10n
i) ii) 1 iii) 1 iv) 1 million 1 32 5
103 tn 7 x2 10 p2 8 m5 3 y
Index Laws 1 53 1
105 1 82 1 xm
3-2
5-1
10-3
t -n
7x-2
10p-2
8m-5
3y-1 1
125 25 4 5 24
2-1
2-4
-23
103
10-1
10-2
106