What is Exponential Form | How to Write Numbers in Exponential Form?

What is Exponential Form?

We all must have heard the word “exponential” before. What does this word mean? Exponential means to become more and more rapid in growth. However, in mathematics, it represents a mathematical expression that has one or more exponents. Hence, we know it as an exponential form.

We can say that a thing may increase with an exponential rate when the increase becomes quicker and quicker as the thing which is talked about becomes larger.

Now let us learn more about the exponential form of numbers which is greatly used and applied in mathematics.

Source: VirtualNerd

Exponential Form

As we discussed earlier that it involves a number of the numerical terms expressed in exponents. Let us take the example of the number 1000.

We can write 1000 as 10x10x10, but instead of writing 10 three times we can write the number 1000 in an alternative way too.

1000 = 10 x 10 x 10

1000 = (10)³………..(exponential form)

Let us take another example to further clarify the concept of expressing a number in exponential form.

Let us take the example of a number 576895.

Now we can express this number in the following ways

576895 = 5×100000 + 7×10000 + 6×1000 + 8×100 + 9×10 + 5×1
576895= 5 x 10⁵+ 7×10⁴ + 6×10³ + 8×10²+ 9×10¹+ 5x 10⁰

The last term which includes 10⁰can simply be written as 1 because any number when expressed raising it to the power of 0 it equals 1.

Therefore we can clearly say that exponents simply refer to how many times a particular number appears in a numerical term.

Let us take the example of number 32. We can write the number 32 in any one of the following ways

32= 2x2x2x2x2

32= 2⁵

When we express a number in the exponential form then we can say that its power has raised by the exponent. In the above-mentioned example, 2⁵will be called as 2 to the power 5 or 2 raised to the power of 5.

How to Write a Number in Exponential Form?

As we discussed earlier that it is nothing but simply to express a numerical term raised to certain powers of its prime factors based on the following way:

Source: Quora

Base Exponent

Therefore, to express a number in exponential form the very first step is to write the number as the product of its prime factors.

Let us take the example of the number 1260.

When we express 1260 as a product of its prime factors then we can write it as

1260= 2x2x3x3x5x7

However, in the exponential form, the same number can be:

1260= 2² x 3² x5¹x7¹

Therefore, we can see that expressing a number in its exponential form can be an easier task and it also saves time and space while writing.

Therefore we may conclude that whole numbers can be expressed in exponential form by raising the powers of their prime factors in which the exponent helps in telling us that how many times the base has been used as a factor.