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Homework Statement
Q7.[/B] a) Express [itex]x[/itex]^[itex](n1)⋅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 noncalculator 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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