SOLUTION: Can't figure this out for the life of me.Thanks in advance (3m^2/3-4m^-1/3) factor out m^-1/3

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Question 837613: Can't figure this out for the life of me.Thanks in advance
(3m^2/3-4m^-1/3) factor out m^-1/3

Found 2 solutions by josh_jordan, Edwin McCravy:
Answer by josh_jordan(263)   (Show Source): You can put this solution on YOUR website!
Hello. This is how it would look if m^(-1/3) was factored out of 3m^(2/3)-4m^(-1/3):



This is why:

When you multiply m^(-1/3) by 3m, you are ADDING the exponents. So, you would add -1/3 and 1, which would be 1 - 1/3 = 2/3, hence 3m^(2/3)

When you multiply m^(-1/3) by 4, you get 4m^(-1/3), which gives you your original equation. So, again, the answer is


Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
 

We can easily factor  out of the second
term.  So the only hitch is in factoring  out of the first term.  

Let's let P be the power of m that we leave inside the parentheses
when we factor  out of the first term.
That is, suppose P is such that the original expression factors 
like this:



Now let's multiply that back out by adding exponents of m 
on the first term:



That has to equal the power of m in the first term of the original:

 

So we must have .  Solve that for P
                
                
                

So we replace P by 1 in



and get:



or just:




Edwin

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