There is no "plain" regex that correctly determines whether a string's length is a square, or one that determines whether a string's length is a power of some other fixed number. The corresponding languages are not regular, and these two examples are typical examples of standard homework problems in a first theory of computation course.
Thus under your constraints, the key to such a regex must be in clever use of backreferences. But it's not clear how backrefs be useful. Backrefs can only really handle linear relations in the length of strings, while exponentiation is highly non-linear.
Are you posting in the right place? Check out Where do I post X? to know for sure.
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
<h5> <h6> <hr /> <i>
<li> <nbsp> <ol> <p>
<small> <strike> <strong>
<sub> <sup> <table>
<td> <th> <tr> <tt>
Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
Want more info? How to link or
or How to display code and escape characters
are good places to start.