my @units= split m#(?<=.)(?:(?=/)|\*)#, $units, -1;
    my %power;
    for my $unit (  @units  ) {
        my $power= 1;
        if(  $unit =~ s#\^(\d+)$##  ) {
            $power= $1;
        }
        if(  $unit =~ s#^/##  ) {
            $power= -$power;
        }
        $power{$unit} += $power;
    }
    # ...