Solve interesting exponential equation in terms of x

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I am having difficulty solving this equation in terms of $x$

$y =\dfrac{x^x}{x^{x^{\frac{x}{k}}}}$

I have been able to re-arrange exponents into the following:

$x^x x^{-\sqrt[k]{x^x}} $

$x^{x - \sqrt[k]{x^x}} $

$xe^{x\ln x - \sqrt[k]{x^x}-\ln x} $

I am not too certain how to proceed. I have read about the Lambert $W$ function, but I don't know how to manipulate variables to reach that point.

Any help is greatly appreciated