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