Indices and Laws of Indices

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Introduction

     If m is a positive integer, a x a x a …. m times is written as a^m. 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".

Indices

     We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
Here 2 is called the base and 6 is called the power (or index or exponent).
We say that "64 is equal to base 2 raised to the power 6".
The Laws of Indices are : Product Law, Quotient Law, Power Law, (ab)^m = a^m . b^m.
An irrational root of a positive rational number is called a surd.

Summary

     If m and n are positive integers, and then

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

     (ii) [Quotient Law]

     (iii) (a^m)ⁿ = a^mn [Power Law].