# Exponent(index) and laws of exponents(indices).

### Exponent or Index:

When a number (let a) is multiplied by itself multiple time(let n times) then we represent this case by adding “n” superscription to “a” as given below:

an

When , a number is repeatedly multiplied by itself the number of times the number is multiplied by itself is called the exponent the the number which is being multiplied is called base or index.

For example:

In an

“a” the index or base and “n” is exponent of the base “a”.

### Laws of Exponents or Indices:

The rules which gives meaning to expression with exponent is known as laws of indices. And the laws of indices are:

1. an = a×a×a×…………..nth Term

2. a-n=1/an

3. $a^{p/q} = \sqrt[q]{a^p} \cdots ( q \in N \backslash \{ 0 \} , p \in Z )$

4.  ap / aq = ap-q

5. am×an=am+n

Note: $a^{p/q} \neq a^p / a^q$

Many thanks to Co. H . Tran  for his help to make this page better.

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