DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "contextLimitedPowers.pl",
  "PGML.pl"
);

Context("Numeric");
LimitedPowers::OnlyPositiveIntegers();

TEXT(beginproblem());

# counts the number of occurances of $needle in $haystack
sub count {
  my ($needle, $haystack) = @_;
  my $count = () = $haystack =~ /~~Q$needle~~E/g;
  return $count;
}

$var = "x";
$m = 4;
$n = 9;

$diff = $n - $m;

$ans = Formula("1/$var^{$diff}");

$ans = $ans->cmp(
  checker => sub {
    my ($correct, $student, $self) = @_;
    my $str = $self->{original_student_ans};
    Value->Error("Remember to simplify!") if count($var, $str) > 1;
    return $correct == $student;
  }
);

BEGIN_PGML

Simplify the following fraction without using negative exponents.

[`\dfrac{[$var]^[$m]}{[$var]^[$n]} = `] [__]{$ans}

END_PGML

ENDDOCUMENT();