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I have read many other solutions but this situation seems unique.

\documentclass{exam}
\usepackage{multicol}
\usepackage{amsmath}
\begin{document}
 \begin{questions}
\question Simplify the following:
    \begin{multicols}{4}
        \begin{parts}
            \part $8^\frac{2}{3}$
            \part $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$ 
            \part $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
            \part $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
        \end{parts}
    \end{multicols}
 \end{questions}
\end{document}
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up vote 7 down vote accepted

The heights of the four part letters is different, because the different heights of the formulas. The following example defines \vphantomB with an invisible box of the greatest height of part (b):

\documentclass{exam}
\usepackage{multicol}
\usepackage{amsmath}
\begin{document}
 \begin{questions}
\question Simplify the following:
    \begin{multicols}{4}
        \def\vphantomB{\leavevmode\vphantom{$\dfrac{16^{\frac{2}{3}}}{}$}}
        \begin{parts}
            \part \vphantomB $8^\frac{2}{3}$
            \part $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$
            \part \vphantomB $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
            \part \vphantomB $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
        \end{parts}
    \end{multicols}
 \end{questions}
\end{document}

Result

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you can use the package enumitem instead:

documentclass{exam}
\usepackage{amsmath}
\usepackage[inline]{enumitem}
\begin{document}
 \begin{questions}
\question Simplify the following:

\begin{enumerate*}[label*=(\alph*),itemjoin={\hfill}]
  \item $8^\frac{2}{3}$
  \item $\dfrac{16^{\frac{2}{3}}}{16^{\frac{1}{6}}}$ 
  \item $9^\frac{1}{3}\cdot 9^{-\frac{5}{6}}$
  \item $\left(25^{\frac{1}{3}}\right)^{\frac{3}{2}}$
\end{enumerate*}
\end{questions}

\end{document}

enter image description here

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In this solution, if you have too many items, there is no vertical alignment betwen the items in different lines. – Bernard Apr 24 '14 at 12:01

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