You can
put this solution on YOUR website!I'll take a crack at it.
Your problem is:
(x^{a+b})^{a-b}
-----------------
(x^{a-2b})^{a+2b}
A couple of basic concepts should help you. There is no relationship between any of the variables shown below and the ones in your problem.
Concept 1.
Concept 2.
Concept 3.
Back to your problem which is to simplify:
Use concept 1 to make your equation equal to:
When you multiply (a+b) * (a-b) you get a^2 - b^2
When you multiply (a+2b) * (a-2b) you get a^2 - 4b^2
Your equation becomes:
Using concept 2, we change this equation to be equivalent to:
Using concept 3, we change this equation to be equivalent to:
The x^(a^2) cancels out and the x^(4b^2) / x^(b^2) becomes:
x^(4b^2 - b^2) which becomes x^(3b^2) using concept 2.
You are left with:
as your answer.
To see if this is correct, we assign some values at random to the original equation and the final equation to see if they are equivalent.
I assigned values of:
a = 5, b = 2
and:
a = 2, b = 2
and:
a = 2, b = 3
and confirmed that the original equation and the final equation are equivalent.
I think the answer is good.
The answer is:
