Lining up sub and superscripts

How about:

$ {{b_{(1)}}^{(1)}}{}_{(1)} $

In your code, the second subscript is appended to the entire preceding formula, hence it is placed lower than anything in that formula. So, I just appended that second subscript to empty brackets instead, and it seems to deliver:

You can use the tensor package:

\documentclass{article}
\usepackage{amsmath,tensor}

\begin{document}

\[
\tensor{b}{^{(1)}_{(1)}^{(1)}}
\]

\end{document}