Approximately how many times greater is 1.2×103 than 4×10−1 ?

3000 Quick answer
Let your calculator do the work. Be careful how you enter this in. (Are you supposed to estimate it? We'll get around to that.) Write it like this.

1.2 * 10^3 divided by 4 * 10^-1 Your calculator will do this nicely. The trick is the - 1. Put it in the calculator like this.
1.2 
*
10
^
3
=
÷
4
*
10
^
(-1) 
= The calculator should read 3000
That's one way to do it. Another way is just to do it all by hand. The numbers are easy enough
1.2 * 10^3 means shift the decimal 3 places right. 1 200 which is 1200
4 * 10^-1 can be handled 2 ways 10 to the minus 1 in the denominator becomes 10^1 in the numerator. Notice the sign change on the 10 when you shift if :it becomes plus! That's why you did it.

1200 * 10^1 
12000

Now you are still left with 4 in the denominator.
12000/4 = 3000. 

The first method always works. The second one gives you a better understanding of how powers work. There are other ways of doing this, but these are the two best, I think.