\documentclass[preview,border=1pt]{standalone}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{nicefrac}

\begin{document}

\[
\frac{1}{2}=\dfrac{1}{2}=\tfrac{1}{2}=1/2=\nicefrac{1}{2} \qquad 
5^{\frac{2}{3}}=5^{2/3}=5^{\nicefrac{2}{3}}
\]
\end{document}