Index Notation Sunday, 24 February 2019

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

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 11 8𝑑 6 28𝑒 9 7𝑒 8

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

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

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) 9 1 2 (iii) 27 1 3 (iv) 25 − 1 2