DOCUMENT();

loadMacros('PGstandard.pl', 'MathObjects.pl', 'PGML.pl', 'contextLimitedPowers.pl', 'answerHints.pl', 'PGcourse.pl');

# Setup

LimitedPowers::OnlyPositiveIntegers();

$var = list_random('a', 'b', 'x', 'y');
Context()->variables->are($var => 'Real');

$n    = random(2,  4);
$m    = random(-9, -5);
$num1 = random(2,  5);
$num2 = random(-5, -2);

$ans = Compute("$num1 * $num2 / $var^(-$n - $m)")->reduce;

$ans_cmp = $ans->cmp->withPostFilter(AnswerHints(
	sub {
		my ($correct, $student, $ansHash) = @_;
		# Count the number of variables (Better if checked for reduced constants too.)
		my $CorrectVariableNumber = $correct =~ tr/a-zA-Z//;
		my $StudentVariableNumber = $student =~ tr/a-zA-Z//;
		return $ansHash->{score} == 1 && $CorrectVariableNumber < $StudentVariableNumber;
	} => [
		'Simplify your answer.',
		checkCorrect => 1,
		score        => 0
	]
));

# Main text
BEGIN_PGML
Simplify the expression:

[`([$num1] [$var]^{[$n]})([$num2] [$var]^{[$m]}) =`] [_]{$ans_cmp}
END_PGML

ENDDOCUMENT();