"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:
Each of these is a multiple of the number with a 1 in front:
and each of these is a power of ten, so you can write the exponent which
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.
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.