Help with a simplifying question

[Matt2015]

Hello, I have recently begun taking an advanced Functions course and I find myself stumped on a question. The course is online so its tough to get the needed help, hopefully I can find some here.

The question I have is:

Simplify the following, Express all answers with positive exponents if possible.

(X^a+b)^a-b
------------
(X^a-2b)^a+2b

I am pretty stuck with this, if anyone can give me a hand it would be great to learn how this can be simplified and what steps you take.

Thank You!

 

[Steven G]

Hello, I have recently begun taking an advanced Functions course and I find myself stumped on a question. The course is online so its tough to get the needed help, hopefully I can find some here.

The question I have is:

Simplify the following, Express all answers with positive exponents if possible.

(X^a+b)^a-b
------------
(X^a-2b)^a+2b

I am pretty stuck with this, if anyone can give me a hand it would be great to learn how this can be simplified and what steps you take.

Thank You!

You need two hints to solve this one.

1) (x^y)^z = x^(yz) regardless of what y and z are (hint: y = a+b and z= a-b)

2) (x^y)/(x^z) = x^(y-z)

 

[Matt2015]

I appreciate the speedy response. However, I am still a little bit confused.

You mention that (X^Y)^Z = X^(YZ) but that is the part that actually confuses me. When I see (A-B,A+B) what is the result?

Right now the only thing I can think of with this is the result being

X⁴

but I know this is incorrect.

I get

(X^A2+4B2)
----------
(X^A2+B2)

Which leads me to X^​4

 

[Matt2015]

That's what I do.. but I don't think I am correct, can anyone tell me what part I am doing wrong? I apologize for being a nuisance but I spent several hours on this yesterday and still remain lost.

(X^a-b)^a+b

---

(X^a-2b)^a+2bTurns into


X^(A²-B²)

---

X^(A²-4B²)


From here I flip the fraction because it is a - and then I follow the basic division rules of subtraction. This leads me to an answer of

X^3B^2

But I remain lost on this. B is already squared and it is in the exponent. So you end up with an exponent on an exponent that you cant solve with more multiplication and should there still be an X on top?

As you can tell from my previous reply my thinking keeps changing because I am unsure with this.

 

[Matt2015]

Thank you very much for your help. Just to clarify about my flipping comment.

I was originally instructed that when you have a negative you flipped it up or down to the opposite side of the numerator or denominator. That would make the problem:

x^(a²+4b²)
---------
X^(a²+b²)

Then you would follow the laws of subtraction and end up with the same result. I guess it is because I do not understand why you only brought the denominator up and didn't change the numerator, the result seems the same anyway.

 

[Matt2015]

You are extremely awesome! Thank you so much for the help it is really making the difference for me. I still am a bit confused by this but I believe I am starting to understand slowly. Its the positive and negative signs that now mess me up.