Divide the 2 into the 6 and get 3 on top



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



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



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:



We can eliminate the 1 denominator



By definition we can replace the  by 



By definition we can replace the  by 



Multiply the 3 by the  and get 



Multiply the numerators 3×1 = 3
Multiply the denominators 

Answer:  

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



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:



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

Edwin