# What is an exponential form of a number? In math

Learn and know what is exponential form of a number? In the chapter exponents, we will learn about this form. Expressing a number in the exponential form is easy but it includes a small process. If you know the process then it is easy to write. Before that first we will know about exponent.

Any idea about what is an exponent? Exponent will tell us that how many times the Base should be multiplied. For example, in ${ 3 }^{ 4 }$ notation exponent is 4. So we need to multiply 3, 4 times to get the result. Which means 3 if we multiply 4 times the result is 81. So 81 is written as ${ 3 }^{ 4 }$. Generally, ${ 3 }^{ 4 }$ is called as exponential form of 81. How to define exponential form now we will learn.

## Definition of Exponential form of a number:

Any number which is written in the form of ${ a }^{ c }$ is said to be in exponential form, where “a” is called as “Base” and “c” is called as “Exponent”.

Examples:

The number 64 is written as ${ 8 }^{ 2 }$, now we say ${ 8 }^{ 2 }$ is the exponential form of 64. Now can you find out and say what is the exponential form of the number 343? 343 is expressed as ${ 7 }^{ 3 }$. So the exponential form of the number 343 is expressed as ${ 7 }^{ 3 }$.

Do you know How to write the given number in the exponential form?

See if there is 1024 then how to write this number in exponential form? First apply prime factorization for the given number 1024. We get 2.2.2.2.2.2.2.2.2.2, all these two’s if you multiply we get 1024. How many two’s we having? We have 10 two’s. So the exponential form of the number 1024 is expressed as ${ 2 }^{ 10 }$.

Now let us see what is the exponential form of the number 729? Exponential form of 729 we can express in two ways. ${ 3 }^{ 9 }$ and ${ 9 }^{ 3 }$ both gives 729. So we can write the exponential form of 729 as ${ 3 }^{ 9 }$ or ${ 9 }^{ 3 }$. From this example, we can understand that the exponential form any number can be expressed in more than one way.