# Simplify x^(n-1)⋅³√(y^2/2x^5) into Rationalised Surd Form

1. Aug 22, 2015

### Bill_Nye_Fan

1. The problem statement, all variables and given/known data
Q7.
a) Express $x$^$(n-1)⋅³√(y^2/2x^5)$ in its simplest, rationalised surd form.
b) Given that the solution to part a) is 5, and that $y$ can be expressed as $1/x$^$(6n+5)/4)$, determine the value of $x$. Again, express your answer in rationalised surd form.

*Note, this is a non-calculator question*
2. Relevant equations
None, but I suppose knowledge of the index laws would be needed.

3. The attempt at a solution
I have attached my attempted workings to the sheet. While I believe to have gotten to a reasonable answer, I have no way of checking if I am right (this question has come from a sheet, not a text book). This is by far the hardest problem I've encountered with in dices thus far, so I would be very grateful if anybody could double check my work. Thank you for your time.

#### Attached Files:

File size:
26.3 KB
Views:
59
• ###### 20150822_192947 (2).jpg
File size:
34.9 KB
Views:
63
2. Aug 22, 2015

### Staff: Mentor

You can plug your results in calculators like WolframAlpha to check them.
I don't see obvious mistakes but checking the result with a computer is easier. Some steps look unnecessary.

Edit: Oh, didn't check where the thread was.

Last edited: Aug 22, 2015
3. Aug 22, 2015

### SteamKing

Staff Emeritus
You've posted a math problem in the Intro Physics HW forum, but I've moved to the Pre-Calculus HW forum, where it's a better fit.

In the future, please try to post your HW questions in the appropriate HW forum by subject.