5.1 Indices and Laws of Indices (Part 2)


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   

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