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

[Bill_Nye_Fan]

Homework Statement

Q7.[/B] 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*

Homework Equations

None, but I suppose knowledge of the index laws would be needed.

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 textbook). 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.

 

[mfb]

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.

 

[SteamKing]

Homework Statement

Q7.[/B] 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*

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.