1. Index Notation
Sunday, 24 February 2019

2. 𝐴 𝑚 × 𝐴 𝑛 = 𝐴 𝑚+𝑛 𝐴 𝑚 𝐴 𝑛 = 𝐴 𝑚 ÷ 𝐴 𝑛 = 𝐴 𝑚−𝑛 𝐴 𝑚 𝑛 = 𝐴 𝑚𝑛 Example
𝐴 𝑚 𝐴 𝑛 =
𝐴 𝑚 ÷ 𝐴 𝑛 =
𝐴 𝑚−𝑛
𝐴 𝑚 𝑛 =
𝐴 𝑚𝑛
Example
Simplify each of the following
(i) 𝑥 3 × 𝑥 5
(ii) 3𝑎 2 × 4𝑎 7
(iii) 2𝑦 5 × 7𝑦 3
(iv) 6𝑡 4 × 8𝑡

3. Simplify each of the following (i) 𝑥 8 ÷ 𝑥 5 (ii) 12𝑎 6 ÷ 4𝑎 5
Example
Simplify each of the following
(i) 𝑥 8 ÷ 𝑥 5
(ii) 12𝑎 6 ÷ 4𝑎 5
(iii) 21𝑦 10 ÷ 7𝑦 3
(iv) 60𝑡 24 ÷ 5𝑡 12
(v)
(vi)
(vii)
𝑟 8 𝑟 4
6𝑏 5 2𝑏 3
16𝑑 𝑑 6
28𝑒 9 7𝑒 8

4. Example
Simplify each of the following
(i) 𝑥 3 5
(ii) 𝑦 7 4
(iii) 2𝑥 3 3
(iv) 3𝑦 5 2

5. 1 𝐴 𝑚 𝐴 −𝑚 = Example Simplify each of the following (i) 𝑥 −3
1 𝐴 𝑚
𝐴 −𝑚 =
Example
Simplify each of the following
(i) 𝑥 −3
(ii) 2𝑦 −2
(iii) 3𝑚 −1
(iv) 3 𝑛 −2
(v) 2 𝑥 2 −4

6. 𝐴 1 𝑚 = 𝑚 𝐴 Example Simplify each of the following (i) 𝑥 1 2
𝐴 1 𝑚 =
𝑚 𝐴
Example
Simplify each of the following
(i) 𝑥 1 2
(ii)
(iii)
(iv) 25 − 1 2