A few examples of exponential notation 

Rough Draft 
Whats a 1000 divided by 10?
1,000. / 10. =
10^{3} / 10^{1} =
10^{3  1} =
10^{2} =
100.
Whats a million times a billion? (Here is a list.)
Well, a million is 1,000,000.
So a million times a billion is
1,000,000. × 1,000,000,000. =
10^{6} × 10^{9} =
10^{6 + 9} =
10^{15} =
Oh my, a 1. with 15 zeros, err...
1,000,000,000,000,000.
4,000,000,000 / 100 ?
(4. × 10^{9}) / (1. × 10^{2}) =
(4. / 1.)
× 10^{9}) / (1. × 10^{2}) =
What is 100. × 1,000.?
(1. × 10^{2}) × (1. × 10^{3})
Here is what makes it easier: 10^{a} × 10^{b} = 10^{ a + b }!
(Dividing is similar, 10^{a} / 10^{b} = 10^{ a  b })
So... 10^{2} × 10^{3} = 10^{ 2 + 3 } = 10^{5}, and
100. × 1,000. =
(1. × 10^{2}) × (1. × 10^{3}) =
(1. × 1.) × 10^{5} = 1. × 10^{5}
= 100,000.
Sorry, I've made this difficult.
Since 100. is 1. × 10^{2}, you would really just say
100 = 10^{2}.
So 100 × 1000 = 10^{2} × 10^{3} =
10^{2 + 3} = 10^{5} = 100,000.
I mixed in the 1.'s so you could do things like 600 × 4000.
(6. × 10^{2}) × (4. × 10^{3}) =
(6. × 4.) × 10^{2 + 3} =
24. × 10^{5} = 2,400,000.
You could even divide them. Whats 600 / 4000?
(6. × 10^{2}) / (4. × 10^{3}) =
(6. / 4.) × 10^{2  3} =
3/2 × 10^{1} =
1.5 × 10^{1} = .15
(Though we usually write 0.15 to make sure noone overlooks the decimal.)
Comments encouraged.  Mitchell N Charity <mcharity@lcs.mit.edu>) 
Overhaul or punt. Seems of little value as is.