Indices
Index
If a is multiplied by itself n times and a ≠ 0, then a is called the base and n is called the index or power.
a × a × ... n times = an.
Examples
2-1 = 1/2 = 0.5
20 = 1
21 = 2
22 = 2 × 2 = 4
23 = 2 × 2 × 2 = 8
210 = 1024
Laws of Indices
1.a0 = 1
2.a1 = a
3.am × an  =  am + n
4.
am an
 =  am − n
5.(am)n  =  am × n
6.(a × b)n  =  an × bn
7.n a × b  =  n a   ×  n b
8.(
a b
) n  = 
an bn
9.a− n  = 
1 an
10.a1/n  =  n a
11.am/n  =  n am
12.If an = b, then a = b1/n