Why does $\frac{x^{\ln x}}{x}$ simplify to $x^{\ln x -1}$?

Question

The question is basically in the title. Why does $\frac{x^{\ln x}}{x}$ simplify to $x^{\ln x -1}$.

Hoping for a clear explanation.

Answer 1

Because $x^a/x^b=x^{a-b}$ doesn't require $a,\,b$ to be constant.

Answer 2

$$\frac{1}{x}=x^{-1} \\ \frac{x^{\ln x}}{x}=x^{\ln x} \cdot \frac{1}{x}=x^{\ln x} \cdot x^{-1}$$