Laws of Exponents

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1. Oct 25, 2015

Meezus

Hello, this isn't really a physics question but I'm getting pretty desperate and you guys have always been able to help me out before :)

1. The problem statement, all variables and given/known data

http://imgur.com/mYtJDLI

2. Relevant equations
I believe I'm suppose to use the Laws of Exponents.
For the first set possibly but not sure as its addition in the question but can't find any laws with revolve around addition.

for the second set of questions i'm fairly certain its once again but I'm just not 100% sure and I'm also not 100% sure what the question is actually asking.

3. The attempt at a solution
3.2 + 0.007 = 3.27
10 x -4 + 10-2 = 10-6
3.27 x 10-6

for the second set.
82x 2-3=
82= 64
2-3= 0.125
64 x 0.125 = 8
But now I'm not sure what to write, it asks for it as a power of 2? Does it just mean write 23.

If anyone could help would be greatly appreciated.

2. Oct 25, 2015

SteamKing

Staff Emeritus
I don't think the problem wants you to convert 82 and 2-3 to decimals, but instead express each number as a power of 2.

Expressing 2-3 as a power of 2 is easy.

Can you express 8 as a power of 2?

If you can, then what would 82 be expressed as a power of 2?

Once you do this, then what is the product of 82 and 2-3, evaluated using the laws of exponents?

3. Oct 25, 2015

SammyS

Staff Emeritus
That's incorrect. If you check it with a calculator you'll see that.

For sure, 10 x -4 + 10-2 is 1/10000 + 1/100. That definitely is not 1/1000000 .

3.2×10-4 + 0.07×10-2
This similar to adding "like" terms, but those terms are not alike.

Rewrite one or both of them.

For instance, 0.07 = 7×10-2, so 0.07×10-2 = 7×10-2×10-2=7×10-4. Right?

Now both terms are alike, so you can add coefficients.

4. Oct 25, 2015

haruspex

That is completely wrong, I'm sorry to say.
What is 3.2 x 10-4 as a decimal number?

5. Oct 25, 2015

Meezus

Would 82 be 26?
26 x 2-3 = 26+-3

6. Oct 25, 2015

Meezus

0.00032 but people in another thread are telling me not to convert into decimals?

7. Oct 25, 2015

SammyS

Staff Emeritus
Don't post the same thread in more than one place !
Mod note: I merged the two threads into a single thread here.

Last edited by a moderator: Oct 26, 2015
8. Oct 25, 2015

haruspex

For this problem you must do some conversion to decimals, though there is a slightly neater way than I'm suggesting you use. Let's get you to the point of finding the right answer first, then we can revisit that.

9. Oct 25, 2015

Meezus

Ok thanks :)

Last edited by a moderator: Oct 26, 2015
10. Oct 25, 2015

Meezus

Yeah sorry wasn't 100% sure where to post it, so it posted in two places

11. Oct 25, 2015

haruspex

The advice not to convert to decimals was for the second question. For addition and subtraction you do, for multiplication and division you don't.

Last edited by a moderator: Oct 26, 2015
12. Oct 25, 2015

haruspex

It clearly belongs in precalc math, it is not a physics question.
Mod note: Merged the two threads into the one here in precalc.
If you feel it necessary to post on two forums (but it never should be) at least post one thread as a link to the other so that all the responses go on the same thread.

Last edited by a moderator: Oct 26, 2015
13. Oct 25, 2015

Meezus

Oh yes, sorry.

For the first one is it:
3.2 x 10-4 = 0.00032
0.07 x 10-2 = 0.0007
0.00032 + 0.0007 = 0.00102?

14. Oct 25, 2015

haruspex

Yes.
The neater method I mentioned I see has already been described to you by SammyS in the other thread. It consists of extracting a power of 10 as a common factor. This makes the expansion to decimals a bit easier.

15. Oct 25, 2015

SteamKing

Staff Emeritus
Which is?

16. Oct 25, 2015

Meezus

23?

17. Oct 25, 2015

SteamKing

Staff Emeritus
Correct.

18. Oct 25, 2015

Meezus

The question does state to show how I manipulated the powers of 10, would it be possible for you to explain this other method as I don't really understand the other explanation.

Thank you for you help so far :)

19. Oct 25, 2015

haruspex

I'll make it general and see if you can figure out how to apply it to the question.
Suppose you have a.nb+c.nd. Note that the bases of both exponentiated factors are n.
This allows you to take out a common factor of the form nk, for any k you choose.
a.nb=a.nb-k.nk (use the law of exponents you quoted to check this).
a.nb+c.nd=a.nb-k.nk+c.nd-k.nk=(a.nb-k+c.nd-k).nk.
We choose k=d:
(a.nb-d+c).nd.
Now all you have to do is write out a.nb-d as a decimal and add c to it.

20. Oct 26, 2015

Meezus

Sorry for replying so late, this took me a while to understand. Is this correct:
3.2 = 32000 x 10-4
10-4 + 10-4 = 10-8

0.07 = 7 x 10-2
10-2 + 10-2 = 10-4

32000 x 10-8 + 7 x 10-4