SOLUTION: Can you please help with Negative Indices. I have to simplify and express the answer with positive indices. 6m^4n over 2n^3m^6 thankyou

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help with Negative Indices. I have to simplify and express the answer with positive indices. 6m^4n over 2n^3m^6 thankyou      Log On


   

Question 838175: Can you please help with Negative Indices. I have to simplify and express the answer with positive indices.
6m^4n over 2n^3m^6
thankyou
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%286m%5E4n%29%2F%282n%5E3m%5E6%29

Divide the 2 into the 6 and get 3 on top

%283m%5E4n%29%2F%28n%5E3m%5E6%29

The index of m on top minus the index of m on the bottom
gives an index of 4-6 or -2 on top

%283m%5E%28-2%29n%29%2Fn%5E3

The index of n on top is 1 understood, and the coefficient of
n on the bottom is 1 understood

%283m%5E%28-2%29n%5E1%29%2F%281n%5E3%29

The index of n on top minus the index of n on the bottom is
gives an index of 1-3 or -2 on top:

%283m%5E%28-2%29n%5E%28-2%29%29%2F1

We can eliminate the 1 denominator

3m%5E%28-2%29n%5E%28-2%29

By definition we can replace the m%5E%28-2%29 by 1%2Fm%5E2

3%281%2Fm%5E2%29n%5E%28-2%29

By definition we can replace the n%5E%28-2%29 by 1%2Fn%5E2

3%281%2Fm%5E2%29%281%2Fn%5E2%29

Multiply the 3 by the 1%2Fm%5E2 and get 3%2Fm%5E2

%283%2Fm%5E2%29%281%2Fn%5E2%29

Multiply the numerators 3×1 = 3
Multiply the denominators m%5E2%2An%5E2

Answer:  3%2F%28m%5E2n%5E2%29

Note there are many shortcuts and this problem
can be done all in one step!

%286m%5E4n%29%2F%282n%5E3m%5E6%29

Divide the 2 into the 3.
Subtract the smaller index of m from the larger index of m, and
place the result in the bottom because the larger index is on the bottom.
Do the same with the indices of n and write down the answer:

3%2F%28m%5E2n%5E2%29

With that shortcut you don't have to worry about negative indices.

Edwin