SOLUTION: So I have a question i'm doing pre-algebra and i'm having a little trouble so the question is 3m over 15m to the third power and in my book it says something like take the top vari

Algebra ->  Decimal-numbers -> SOLUTION: So I have a question i'm doing pre-algebra and i'm having a little trouble so the question is 3m over 15m to the third power and in my book it says something like take the top vari      Log On


   

Question 548289: So I have a question i'm doing pre-algebra and i'm having a little trouble so the question is 3m over 15m to the third power and in my book it says something like take the top variable subtracted (-) by the bottom variable and usually if its like m we just make it m to the first power but in the book it shows the bottom number (15) as a one (1) well the problem in the book is 5 to the 6th power over 5 to the 8th power and it takes 6-8 and gets -2 so its 5 to the -2nd power over 5 and it changes it to 1 over 5 to the 2nd power and i'm not sure if everyone of the bottom numbers should be changed to 1 or not so yea I tried it and i'm confused and I did all of the other ones and I think I got them right but i'm just stumped by this one and I've tried and tried but i'm stuck so yea please help me. Wow that was a really long run on sentence but yea thanks.
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
Okay I think what you are asking is to simplify
3m%2F%2815m%5E3%29



We have an exponent rule that says something like this:
%28m%5Ea%29%2F%28m%5Eb%29=m%5E%28a-b%29

So all we are doing is using this and a few other tricks
3m%2F%2815m%5E3%29
can be broken up as follows
%283%2F15%29%2A%28m%2Fm%5E3%29
Now 3/15=1/5
and
%28m%2Fm%5E3%29 is just %28m%5E1%2Fm%5E3%29
and using the rule above this is just m%5E%281-3%29=m%5E%28-2%29
So from
%283%2F15%29%2A%28m%2Fm%5E3%29
we get
%281%2F5%29%2A%28m%5E%28-2%29%29
%28m%5E%28-2%29%29%2F5

We could also use the rule
m%5E%28-x%29=1%2F%28m%5Ex%29
to write our answer as
1%2F%285%2Am%5E%282%29%29

Hopefully this helps, please let me know if you are unsure:)