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

  • #1

Homework Statement


Q7.[/B] a) Express [itex]x[/itex]^[itex](n-1)⋅³√(y^2/2x^5) [/itex] in its simplest, rationalised surd form.
b) Given that the solution to part a) is 5, and that [itex]y[/itex] can be expressed as [itex]1/x[/itex]^[itex](6n+5)/4)[/itex], determine the value of [itex]x[/itex]. 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 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.
 

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Answers and Replies

  • #2
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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:
  • #3
SteamKing
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Science Advisor
Homework Helper
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Homework Statement


Q7.[/B] a) Express [itex]x[/itex]^[itex](n-1)⋅³√(y^2/2x^5) [/itex] in its simplest, rationalised surd form.
b) Given that the solution to part a) is 5, and that [itex]y[/itex] can be expressed as [itex]1/x[/itex]^[itex](6n+5)/4)[/itex], determine the value of [itex]x[/itex]. 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.
 

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