Matching what you show as literal text should do the job. You probably want to anchor the beginnning to the start of the string. A literal match like this can be done with substr and eq, too.

my $string = '/sbc/dasds/sdf/dsd/modem';
my $regex = qr!^${string}!;

$_ = '/sbc/dasds/sdf/dsd/modem_50';

if (m/$regex/) {
    print;
    print "\nRegex works\n";
}

if ($string eq substr $_, 0, length $string) {
    print;
    print "\nString equality works\n";
}
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If you're doing this to comb modems out of a bunch of file paths, there is also glob:

my @modems = glob '/sbc/dasds/sdf/dsd/modem*';
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