Trying to find a function

Question

Hello I was looking at where x^n and xn intersect as I was changing n and I realized they made a exponential type pattern so I tried for about 2 weeks to find this function but was not able to do so. I was wondering if this function can’t be normally graphed and if so then can you use it to make other inter sectioning functions of which there intersecting function makes a function that can’t normally be represented here is the problem I was looking at https://www.desmos.com/calculator/8qh8lsmvpj