Move sign under exponent

I could understand a desire to avoid the hole, but your readers would have a hard time in interpreting the expression if the exponent is completely above \times.

I'd possibly use (3) or (4), but would prefer (5), removing the \times altogether, or better yet (6).

Notice the \! in the exponent to avoid the other hole.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}\times\frac{1}{(2k+2)(2k+1)}
\end{equation}

\begin{equation}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}
\mspace{-\medmuskip}
\times \frac{1}{(2k+2)(2k+1)}
\end{equation}

\begin{equation}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}
\mspace{-1.5\medmuskip}
\times \frac{1}{(2k+2)(2k+1)}
\end{equation}

\begin{equation}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}
\mspace{-2\medmuskip}
\times \frac{1}{(2k+2)(2k+1)}
\end{equation}

\begin{equation}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}
\frac{1}{(2k+2)(2k+1)}
\end{equation}

\begin{equation}
\frac{1}{(2k+2)(2k+1)}
\left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\!k+1}
\end{equation}

\end{document}

enter image description here


I personally would not do that but since you are asking...

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amsthm}

\begin{document}

\begin{equation}
    \left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\mathrlap{k+1}} \times \frac{1}{(2k+2)(2k+1)}
\end{equation}

\end{document}

enter image description here


I'm not sure if this is what you mean, but you can do this with the \rlap command.

enter image description here

Here is the code:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amsthm}

\begin{document}

\begin{equation}
    \left(\frac{k+1}{k^\frac{k}{k+1}}\right)^{\rlap{$\scriptstyle{k+1}$}} \times \frac{1}{(2k+2)(2k+1)}
\end{equation}

\end{document}