Exponents are short forms used to represent a set of repeated factors.

$3^{6}$ is used to represent 3 multiplied to itself six times. i.e 3 x 3 x 3 x 3 x 3 x 3. In $3^{6}$, the number 3 is called the Base and the number 6 is called the exponent or power.

The exponent is defined as a number which is used to represent the number of times a given number has to be multiplied by itself. Exponents could also be defined as the operation in raising a particular number to a power in multiplication and in which all the factors are equal.

The expression of 8$^{3}$ means that three 8’s are to be multiplied with each other. Similarly, 6$^{2}$ would mean 6 x 6. The relevant power of any particular number is the number by itself.

The power is defined as the number of times the number is to be taken as one of the factor. The method of finding a root is nothing but the inverse of raising a number to a power.

Exponent is an index of a power. "The exponent is also known as the Powers or Indices".


Exponents

Consider the following:

2 - two occurs once
2 X 2 - two occurs twice
2 X 2 X 2 - two occurs thrice

We can see that the number 2 is multiplied to itself some number of times. If 2 has to be multiplied to itself many times, it would become tough to write the same. So, there is a need to write in some notation.

So, we write 2 multiplied to itself thrice as $2^{3}$

2 - two occurs once $2^{1}$
2 X 2 - two occurs twice $2^{2}$
2 X 2 X 2 - two occurs thrice $2^{3}$