# Thread: Simplifying surds and fractions

1. ## Simplifying surds and fractions

Hi guys,

How would one simplify the following?

(2^n x 4^n+1) / 8^n-2

Also, if x = (√3) + 1 what is the value of x^2 - 1/x^2 with the answer as a simplified surd?

2. ## Re: Simplifying surds and fractions

Originally Posted by Coshy
(2^n x 4^n+1) / 8^n-2
Please use * to represent multiplication; x could be a variable...
Did you mean:
2^n * 4^(n+1) / 8^(n-2) ?
Brackets are VERY important here!
There is a huge difference between 8^n-2 and 8^(n-2); important that you understand that...

3. ## Re: Simplifying surds and fractions

Do you know your rules of exponents? Also, what did you try in solving this problem. Please add some more parentheses, as your notation is a bit confusing on what is the exponent.

4. ## Re: Simplifying surds and fractions

Originally Posted by Coshy
Hi guys,

How would one simplify the following?

(2^n x 4^n+1) / 8^n-2
I presume you mean, as wilmer suggested, ((2^n)(4^(n+1))/8^(n-2). You need to know that 4= 2^2 and 8= 2^3 so 4^(n+1)= (2^2)^(n+1)= 2^(2(n+1))= 2^(2n+2) and 8^(n-2)= (2^3)^(n-2)= 2^(3(n-2))= 2^(3n- 6).

So your problem is ((2^n)(2^(2n+2))/(2^(3n- 6)). Combine those. How many "2"s do you have in the numerator and how many in the denominator?

Also, if x = (√3) + 1 what is the value of x^2 - 1/x^2 with the answer as a simplified surd?
You know that (√3+ 1)^2= (√3)^2+ 2(√3)+ 1, don't you? And (√3)^2= 3 so x^2= 2(√3)+ 4. For 1/x^2= 1/(2(√3)+ 4), "rationalize the denominator": multiply both numerator and denominator by 2(√3)- 4.

(This is the third problem you have posted not showing any attempt to do them yourself. I you honestly have no idea how to even begin any of the exercises you are being given, perhaps this course is too difficult for you.)