Question

Express each of the following numbers using the exponential notation: 729

Answer 1

Hint: The most beneficial way of presenting an exponential notation is to think in terms of even and odd numbers and start with the least one possible so that we can find the answer quickly.

Complete step by step answer:
To simplify the writing and handling of very big numbers, we can express those numbers in terms of the product of small numbers and this is termed as the exponential notation of that number. In this case, we will find the exponential notation of \[729\].
The number in the question is an odd number and so we cannot simplify it with $2$ as the base. So let us start with $3$ and as we move further, we can see that it is divisible by $3$ and not just once. If we continue the process, we can see that the number can be expressed in terms of the product of $3$ for six times. Now the question arrives: how to write it?
 Now suppose that for the number $n$, we can express it as a product of $m$ for $a$ times. Then we call $m$ as the base and $a$ as the exponent and we can write the final result as ${{m}^{a}}$. So in the case of $729$, we can write its exponential notation as ${{3}^{6}}$, where $3$ is the base and $6$ is the exponent.

Note: Now, many might have some confusion as to what ${{3}^{6}}$ means and how it is a product. Then for them, ${{3}^{6}}$ means three multiplied six times. And remember that the number of factors must be a natural number.