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Subject  >  Math  >  Number Theory  >  Indices

Indices

Introduction
       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".
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 = am . bm.
An irrational root of a positive rational number is called a surd.
Summary
       If m and n are positive integers, and then
       (i) am an = am + n [Product Law]
       (ii) [Quotient Law]
       (iii) (am)n = amn [Power Law].

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Indices
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