4.1 Indices and Laws of Indices (Part 2)
(C) Fractional Indices
a1n is a nth root of a. a1n=n√a amn is a nth root of am. amn=n√am
Example 1:
Find the value of the followings:(a) 8112(b) 6413(c) 62514
Solution:
(a) 8112=√81=9(b) 6413=3√64=4(c) 62514=4√625=5
Example 2:
Find the value of the followings:
(a) 1632(b) (2764)23
Solution:
(a) 1632=(1612)3=43=64(b) (2764)23=(3√2764)2=(34)2=916
(D) Laws of Indices
am×an=am+n Example: 33×32 =33+2=35=243
am÷an=am−n or aman=am−n,a≠0 Example: 33÷32 =33−2=31=3 or 3332=33−2=31=3
(am)n=amn Example: (73)4=73×4=712
(ab)n=anbn Example: (15)3=(5×3)3=23×33
(ab)n=anbn, b≠0 Example: (35)4=3454=81625