Hi Kent.

"Exponential form" simply means a numeric form involving exponents.

One way to write such a number is by recognizing that each position represents a power (exponent) of 10. So you can first break it up into separate pieces.

I will use my own number 5 625 702:
5 625 702 = 5 000 000 + 600 000 + 20 000 + 5 000 + 700 + 2

Each of these is a multiple of the number with a 1 in front:
5 625 702
= 5 x 1 000 000 + 6 x 100 000 + 2 x 10 000 + 5 x 1 000 + 7 x 100 + 2

and each of these is a power of ten, so you can write the exponent which
is the same as the number of zeros:

5 625 702 = 5 x 10⁶ + 6 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 7 x 10² + 2 x 10⁰

That last one may not really be necessary. 10^0 is equal to 1, so really we are just saying 2 x 1.

That is one expanded exponential form.

Another way to represent a number using exponents is to write it as a product of prime numbers. Any positive integer above 1 is the product of a unique set of prime numbers.

I know that the number 26 460 is 2 x 2 x 3 x 3 x 3 x 5 x 7 x 7.

So written using exponential form as a product of primes, I write

26460 = 2² x 3³ x 5 x 7²

The exponents reflect how many times that prime number appears as a factor.

There is also an exponential form called "scientific notation" which is used extensively in science. That is simply a matter of counting how many digits you need to move the decimal place in order to have a number between 1 and 9.999...

So for 5 625 702, I would move the decimal place to 5.625 702, which is 6 places leftwards from where it was. Thus, I say that

5 625 702 in scientific notation is writting 5.625 702 x 10⁶.

I hope this gives you a good idea of how to write things in exponential forms.

Cheers,
Stephen La Rocque.