Perl has so many ways of quoting things, you never have to escape characters.

1) Use the here doc syntax for your string, which will get rid of the outer double quote marks--allowing you to use double quote marks inside your string.

2) Use qr{ } around your whole regex, which will get rid of the beginning and ending forward slash marks(/)--which will allow you to use forward slash marks inside your regex.

3) Inside a regex, a single quote mark has no special meaning (same for a double quote mark), so you don't have to escape it.

4) It's usually more efficient to use:

[^some_char]some_char
[download]

than:

 .*?some_char
[download]

Here is an example:

use strict; 
use warnings; 
use 5.012;

my $string = <<END_OF_HTML;
<ul>
  <li>
    <div id="Show1400">
      <a href="../../../KeyboardKeys/RetainerClip/Acer/Aspire/1400">14
+00</a>
    </div>
  </li>
  <li>
    <div id="Show1410">
      <a href="../../../KeyboardKeys/RetainerClip/Acer/Aspire/1410">14
+10</a>
    </div>
  </li>
</ul>
END_OF_HTML

my $regex = qr{<a href=["']([^"']+)["']>[^<]+</a>};

while ($string =~ /$regex/g) {
    say $1;
}

--output:--
../../../KeyboardKeys/RetainerClip/Acer/Aspire/1400
../../../KeyboardKeys/RetainerClip/Acer/Aspire/1410
[download]