A teaching question. What is or might be simplest form for rational exponents? My search turns up little for the concept other than a translation of the simplest form for n-th root radicals. But that leads to ugly things such as...
$\large{5^\frac{7}{3}\rightarrow 5^2\centerdot 5^\frac{1}{3}}$
$\large{x^{-\frac{2}{3}}\rightarrow x^{-1}\centerdot x^\frac{1}{3}}$
...when the whole point of rational exponents is beauty and elegance.