# Dividing Powers

1. Dec 31, 2009

### Gringo123

Can anybody talk me through the righ way to approach this problem? I know that the answer is 8.79 x 10 to the power of 5.

7.23 x 10 to the power of 5 x 1.09 x 10 to the power of minus 3
______________________________________________________ (divided by)

8.97 x 10 to the power of minus 4

Thanks

2. Dec 31, 2009

### sjb-2812

What is 102 x 10-3, for instance?

3. Dec 31, 2009

### Gringo123

10-1 (to the power of minus 1)??

4. Dec 31, 2009

### sjb-2812

Yes, that's right! So what would 10a x 10b be (where a and b are any number)?

5. Dec 31, 2009

### Gringo123

My understanding is that you add the powers but use normal multiplication with the main numbers. So would it be: 100 a+b (a+b as powers)?

6. Dec 31, 2009

### sjb-2812

Not quite, otherwise in your first example you would have written 100-1, wouldn't you?

7. Dec 31, 2009

### Gringo123

10 a+b

8. Dec 31, 2009

### sjb-2812

Got it! So how about 106/102 ?

9. Dec 31, 2009

### Gringo123

To divde you suntract the powers so, 10 4?

10. Dec 31, 2009

### sjb-2812

Going well so far, so 10a/10c = ?

11. Dec 31, 2009

### Gringo123

10 a-c

12. Dec 31, 2009

### sjb-2812

Yeap, so 10a x 10b / 10c = ?

13. Dec 31, 2009

### Gringo123

10 a+b-c?

14. Dec 31, 2009

### sjb-2812

Indeed, so 105 x 10-3 / 10-4 = ?

15. Dec 31, 2009

### Gringo123

10 5 x 10-3 = 10 2
10 2 / 10 -4 = 10 -2

16. Dec 31, 2009

### sjb-2812

No, remember for division 10a/10c you subtract c from a, as per posts 8 to 11, so 102/10-4 = ?

17. Dec 31, 2009

### Gringo123

But 2 - 4 = -2 so why is it incorrect to say 10 2 / 10 -4 = 10 -2? All I have done is to subtract -4 from 2.

18. Dec 31, 2009

### sjb-2812

You are not doing the sum 2 - (+)4, you are doing 2 - -4. Perhaps another way to look at it is how much warmer is 2°C than -4°C? Is that 2°C ?

19. Dec 31, 2009

### Gringo123

No, it is 6°C. I know that 2 - (-4) = 6 so is the answer to 10 2 /10 -4 = 10 6?
Thanks for your help and patience by the way!

20. Dec 31, 2009

### Gringo123

I'm starting to get it now and I can see where I went wrong the 1st time.
If you work out the decimal figures and the figures with powers separately you get;
0.879 x 10 to the power of 6.
In order to present the answer as a number larger than 1 we have remove one of the powers and used it to multiply 0.879 by 10, leaving us with 8.79 x 10 5.
Thanks again for all your help and patience.