1. Index Laws
Objectives:
A Grade Use Index Notation and Index Laws for
Fractional Powers such as 16
A* Grade Use Index Notation and Index Laws for
Fractional Powers such as 16
Prior knowledge:
Understand :
Use Index Laws for positive and negative powers

2. Index Laws
Using the index laws to simplify
a3 × a4
a3+4 = a7
Understanding that we add the index numbers we can
deduce the meaning of:
100½ × 100½
By adding the index numbers
100½+½ = 1001 = 100
Therefore 100½ is a number, that, when multiplied by itself is 100.
We know that:
√100 × √100 = 100
Therefore:
100½ = √100
The general rule is:
x½ = √x

3. The general rule is: x = a√x Index Laws
Understanding that we add the index numbers we can
deduce the meaning of:
x × x × x
By adding the index numbers
= 1001 = 100
3√100 × 3 √100 × 3 √100 = 100
Therefore:
= 3√100
The rule is:
x = 3√x
x = a√x
The general rule is:

4. Now do these:
1. Evaluate
a) 4½ b) 40 c) 8 d) 125
2. Evaluate
a) 32 b) c) 512 d)
Index Laws 2 1 2 5 2 3 8 9

5. Index Laws
More complex fractional index laws together:
(73)2 means
(73) × (73)
= 73+3
= 76
= 4
(4½)3 means
4½ × 4½ × 4½ 4
Therefore when we see
We know it means (4½)3
In general a actually means (4 )y

6. Now do these:
1. Evaluate
a) 4 b) 27 c) 16 d) 125
2. Evaluate
a) 64 b) c) 512 d) 6561
Index Laws 8 9 8 25 32 81 64
729

7. Now do these:
3. Evaluate
a) -8 b) (-125) c) 4 d)
e) f) g) × 8
h) 49 × i) 5-2 × 105 × 16
Index Laws 8 25
100
114
1000