# Learn Exponent with Examples

##### What is Exponent?

The base n raised to the power of a is equal to the multiplication of n, a times:

na = n × n × … × n (a times)

There:

• “n” is the base and
• “a” is the exponent

or

An exponent refers to the number of times a number is multiplied by itself.

##### An example of exponent

3 to the 4th, written as 34 means:

$\dpi{120}&space;\fn_jvn&space;\large&space;3\times3\times3\times3\times&space;=&space;81$

34 is not equal to 34 = 12

##### Special Cases
1. Exponent is 0:

n = 1

When the exponent is zero, as in 5, the result is always equal to 1.

5 = 1

26,981 = 1

##### 2.Exponent is negative

n-a = 1 / na

When an exponent is a negative integer, the result will always be a fraction. Fractions contain a numerator and a denominator. In this case, the numerator is always 1. To calculate the denominator, assume that the negative exponent is positive, and raise the number to that power, like this:

5-4 = 1 / 54

##### Some Important Rules for Exponents

Product rule with the same base

na.nb = na+b

Example:

45 . 46 = 4 5+6 = 4 11 = 4194304

##### Product rule with the same exponent

na . ma = (n.m)a

Example:

1. 26. 36 = (23)6 = 66 = 36
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##### Quotient rule with the same base

na / nb = na-b

Example:

46 / 45 = 46-5 = 41 = 4

##### Quotient rule with the same exponent

na / ma = (n/m)a

Example:

106 / 56 = (10/5)6 = 26 = 64

##### Power rules #1

(na)b = na.b

Example

(32)3 = 32*3 = 36 = 729

##### Power rule 2

Example

= 4 (2^3) = 48 = 6561