5.1 Indices and Laws of Indices (Part 2) Posted on April 21, 2020 by user 5.1 Indices and Laws of Indices (Part 2) (C) Fractional Indices a 1 n is a n th root of a . a 1 n = a n a m n is a n th root of a m . a m n = a m n Example 1: Find the value of the followings: (a) 81 1 2 (b) 64 1 3 (c) 625 1 4 Solution: (a) 81 1 2 = 81 = 9 (b) 64 1 3 = 64 3 = 4 (c) 625 1 4 = 625 4 = 5 Example 2: Find the value of the followings: (a) 16 3 2 (b) ( 27 64 ) 2 3 Solution: (a) 16 3 2 = ( 16 1 2 ) 3 = 4 3 = 64 (b) ( 27 64 ) 2 3 = ( 27 64 3 ) 2 = ( 3 4 ) 2 = 9 16 (D) Laws of Indices a m × a n = a m + n Example: 3 3 × 3 2 = 3 3 + 2 = 3 5 = 243 a m ÷ a n = a m − n or a m a n = a m − n , a ≠ 0 Example: 3 3 ÷ 3 2 = 3 3 − 2 = 3 1 = 3 or 3 3 3 2 = 3 3 − 2 = 3 1 = 3 ( a m ) n = a m n Example: ( 7 3 ) 4 = 7 3 × 4 = 7 12 ( a b ) n = a n b n Example: ( 15 ) 3 = ( 5 × 3 ) 3 = 2 3 × 3 3 ( a b ) n = a n b n , b ≠ 0 Example: ( 3 5 ) 4 = 3 4 5 4 = 81 625