I have no idea where to begin.

[Kian McGrath]

Given that (√y/x)⁻⁵ = x‴/y‴ where x ≠ y
find the value of m

 

[tkhunny]

I presume it should appear as [math]\left(\sqrt{\dfrac{y}{x}}\right)^{-5} = \dfrac{x^{m}}{y^{m}}[/math]

Hint: [math]\sqrt{a} = a^{1/2}[/math]

 

[Steven G]

... and for example \(\displaystyle (a^\frac{1}{2})^7 = a^{(1/2)(7)} = a^\frac{7}{2}\)

 

[JeffM]

The very first thing I would do is a u-substitution, a very helpful technique that for some reason is scarcely taught in algebra.

[MATH]\text {Let } u = \dfrac{y}{x} \implies \dfrac{x}{y} = \dfrac{1}{u}.[/MATH]
[MATH]\therefore \left ( \sqrt{\dfrac{y}{x}} \right )^{-5} = \dfrac{x^m}{y^m} = \left ( \dfrac{x}{y} \right )^m \implies (\sqrt{u})^{-5} = \left ( \dfrac{1}{u} \right )^m = \dfrac{1}{u^m}.[/MATH]
[MATH]\therefore \dfrac{1}{u^m} = (\sqrt{u})^{-5} = \dfrac{1}{(\sqrt{u})^5}.[/MATH]
Now what?