EDIT: I'm an idiot--. I don't know how I messed up the code that badly. Yes, order from left to right does matter (at least for multiplication / division). Here's the fixed version:

use strict;
use warnings;

while (<DATA>) {
    chomp;
    print process($_), "\n";
}

sub process {
    my $exp = $_[0];
    1 while $exp =~ s/\(([^(]*)\)/reduce($1)/eg;
    $exp = reduce($exp);
    $exp =~ s/\s+//g;
    return reduce($exp);
}

sub reduce {
    my $exp = $_[0];
    1 while $exp =~ s{(\d+)\s+([*/])\s+(\d+)}
                     {$2 eq '*' ? $1*$3 : $1/$3}e;
    1 while $exp =~ s{(\d+)\s+([+-])\s+(\d+)}
                     {$2 eq '+' ? $1+$3 : $1-$3}e;
    return $exp;
}

__DATA__
(7 * 3) + (2 + 1)
4 * (5 / (3 + 2)) - 6
2 * 2 * 2
8 / 2 * 3
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