How can I anchor TikZ matrix cell contents to 'baseline' without shifting cell location?

Question

The cells in my tables often contain expressions with superscripts. This results in a text baseline that appears to "wander" between adjacent cells. For example

\begin{tikzpicture}[every node/.style={minimum size=7mm}]
\matrix{
    \node[fill=gray!10]{$a$};  &  \node[fill=gray!20]{$a^2$};  &  \node[fill=gray!30]{$b$}; &  \node[fill=gray!40]{$b^2$}; \\};
\end{tikzpicture}

produces

I understand that the way to align the text of all cells to a common baseline is to use anchor=base, but this has the side effect of jumbling the cells. For example

\begin{tikzpicture}[every node/.style={anchor=base,minimum size=7mm}]
\matrix{
    \node[fill=gray!10]{$a$};  &  \node[fill=gray!20]{$a^2$};  &  \node[fill=gray!30]{$b$}; &  \node[fill=gray!40]{$b^2$}; \\};
\end{tikzpicture}

produces

Is there a way to align all text to a common baseline, without shifting the cells as well?

---

\documentclass[]{article}

\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[every node/.style={minimum size=7mm}]
\matrix{
    \node[fill=gray!10]{$a$};  &  \node[fill=gray!20]{$a^2$};  &  \node[fill=gray!30]{$b$}; &  \node[fill=gray!40]{$b^2$}; \\};
\end{tikzpicture}

\begin{tikzpicture}[every node/.style={anchor=base,minimum size=7mm}]
\matrix{
    \node[fill=gray!10]{$a$};  &  \node[fill=gray!20]{$a^2$};  &  \node[fill=gray!30]{$b$}; &  \node[fill=gray!40]{$b^2$}; \\};
\end{tikzpicture}

\end{document}

Answer 1

You may fix height and depth of text:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}[every node/.style={anchor=base,
    text height=.8em,text depth=.2em,minimum size=7mm}]
  \matrix{
    \node[fill=gray!10]{$a$};&
    \node[fill=gray!20]{$a^2$};&
    \node[fill=gray!30]{$b$}; &
    \node[fill=gray!40]{$b^2$};\\
  };
\end{tikzpicture}
\end{document}