Indices and laws of indices

 If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent".

When the power or index is a fraction say then and it is a surd of order n.
In this chapter we will study the laws of indices.

Indices

     Laws of Indices: If m and n are positive integers, and then

     (i) a^m aⁿ = a^{m + n} [Product Law]

     (ii) [Quotient Law]

     Surd: An irrational root of a positive rational number is called a surd.

Summary

     1) a^maⁿ = a^m+n

     2) a^m/aⁿ = a^m-n

     3) (a^m)ⁿ = a^mn