Question 631007
{{{(l^(2m)(2-m))/(l^3(m-2))}}}
Since one to <i>any</i> power is 1, this simplifies to:
{{{(2-m)/(m-2)}}}
The next step is quick if you notice that 2-m and m-2 are negatives of each other. In one the 2 is positive and in the other the 2 is negative. In one the m is negative and in the other the m is positive. So 2-m and m-2 are negatives of each other. (Let that sink in for a while. It can be helpful in other situations, too, to realize that a-b and b-a are negatives of each other.)<br>
And what do you get when you divide negatives? What is -1/1, 20.3/(-20.3), x/(-x), etc.? Answer for all: -1. So (2-m)/(m-2) is:
-1<br>
P.S. In the future, please explain the expression has an "el" in it to avoid confusion. Here's a solution using el's:
{{{(l^(2m)(2-m))/(l^3(m-2))}}}
We can "un-multiply" the fractions so that you can see better how this works out:
{{{(l^(2m)/l^3)*((2-m)/(m-2))}}}
The (2-m)/(m-2) still works out to be -1. To divide the el's, we use the rule for exponents when dividing expressions with the same base: Subtract the exponents:
{{{l^(2m-3)*(-1)}}}
or just
{{{-l^(2m-3)}}}