# Exponential form

A mathematical notation of expressing a quantity as a number raised to the power of another number is called the exponential form and it is also called as exponential notation.

## Introduction According to the exponentiation, a quantity is split as factors on the basis of a number. They are arranged in a special mathematical form to represent the quantity mathematically.

The number of multiplying factors is displayed as superscript of the number which is considered to split the quantity. This special mathematical notation represents the quantity and it is called exponential form.

### Example

$32$ is a number. It can be written as number of multiplying factors on the basis of number $2$.

$32 = 2 \times 2 \times 2 \times 2 \times 2$

$\implies 32 = \underbrace{2 \times 2 \times 2 \times 2 \times 2}_5 \, factors$

The total number of multiplying factors of $2$ is $5$ in this case. So, write the base number $2$ first and then the total number of multiplying factors as its superscript.

$\implies 32 = 2^5$

The representation of the term $2^5$ is called the exponential notation or exponential form of $32$ on the basis of number $2$.

#### More Examples

Observe the following examples to learn how to write any number in exponential form on the basis of a number.

$(1) \,\,\,$ $81 = 3 \times 3 \times 3 \times 3 = 3^4$

$(2) \,\,\,$ $125 = 5 \times 5 \times 5 = 5^3$

$(3) \,\,\,$ $81 = 9 \times 9 = 9^2$

$(4) \,\,\,$ $16807 = 7 \times 7 \times 7 \times 7 \times 7 = 7^5$

$(5) \,\,\,$ $1771561 = 11 \times 11 \times 11 \times 11 \times 11 \times 11 = 11^6$

##### Terminology

The exponential notation consists of two parts and they are called by two special names.

A number which is used to expand any number in its terms.

The number of times a number is multiplied to itself to obtain another number.

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