1. Indices – The Six Basic Index Laws 1 st Law 5 3 x 5 4 = (5 x 5 x 5) x (5 x 5 x 5 x 5)= 5 7 Example: aax=a + mnmn

2. Indices – The Six Basic Index Laws 2 nd Law 7 5 ÷ 7 2 == 7 3 Example: aa÷=a mn - mn 7 x 7 x 7 x 7 x 7 7 x 7

3. Indices – The Six Basic Index Laws 3 rd Law (3 2 ) 4 = (3 x 3) x (3 x 3) x (3 x 3) x (3 x 3) = 3 8 Example: a= a m n xm n

4. Indices – The Six Basic Index Laws 4 th Law Consider the sequence: Example: 2 3 2 2 2 1 2 0 2 -1 2 -2 8 4 2 1 ½ ¼ a= a m 1 - m

5. Indices – The Six Basic Index Laws 5 th Law Consider the calculations: Example: 3 1/2 x 3 1/2 a=√a√a n = 3 1 = √3 x √3 1 n ‘the n th root of a’ = 3

6. Indices – The Six Basic Index Laws 6 th Law Example: 4 3/2 a= ( √a ) n = (√4) 3 = 8 m n m = (4 1/2 ) 3 ‘the n th root of a to the power of m’