What I would do for something like this is have a limited number of operators, then scan for each and do the right thing. For example,

$operator = <STDIN>;
chomp $operator;
if ($operator eq '+')
{
   $result = $a + $b;
}
elsif ($operator eq '-')
{
   $result = $a - $b;
}
elsif ($operator eq '*')
{
   $result = $a * $b;
}
else
{
   die "unknown operator \"$operator\"\n";
}
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I'm more comfortable with code like that because it leaves less room for unexpected errors from bad input.
But you can do what you're looking for with something like this, using eval:

$first=<STDIN>;
$second=<STDIN>;
$operator=<STDIN>;
chomp $first;
chomp $second;
chomp $operator;

$expression = "$first $operator $second";
print "$expression:\n";

$result = eval $expression;
if ($@)  # ($@ is set by eval if something went wrong)
{
    print "oh no!: $@\n";
}
else
{
    print "$result\n";
}
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By the way, you shouldn't get into the habit of using $a and $b as variable names, since those two variables have special meaning for perl's sort function.