How old is the expanded notation method work

Well, 
For example 

2.34 * 10^6 will be
2,340,000
It is because if you have the positive powers, you move your decimal to the right. In this case the power is 6 so you move your decimal to the right 6 times. 
Here's another example

1.23 X 10^-2 
The answer will be 0.0123 because you move your decimal two the left two times. The power is negative 2 so you move it to the left.

Final tips: If you have positive power, move it to the right and if you have negative power, move it to the left.