##DESCRIPTION
## Simplify Exponents
## 
##ENDDESCRIPTION
## DBsubject(Algebra)
## DBchapter(Properties of exponents, rational exponents and radicals)
## DBsection(Properties of exponents)
## Institution(The College of Idaho)
## Author(RA Cruz)
## MLT(Mult_exponents_one_var)
## MLTleader(1)
## Level(2)
## MO(1)
## TitleText1('Essentials of Intermediate Algebra')
## AuthorText1('Blitzer')
## EditionText1('1')
## Section1('1.6')
## Problem1('')
## KEYWORDS('real numbers','algebraic expressions')
## Date: 2007/09

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "contextLimitedPowers.pl",
  "answerHints.pl",
  "CofIdaho_macros.pl",
  "PGcourse.pl"
);

TEXT(beginproblem());

######################################
#  Setup

@alphabet = ("a","b","x","y");
$choose = random(0,2,2);
@var = ($alphabet[$choose]);
Context()->variables->are($var[0]=>'Real');

$n = random(2,4,1);
$m = random(-9,-5,1);
$num1 = random(2,5,1);
$num2 = random(-5,-2,1);

######################################
#  Main text

BEGIN_TEXT
Simplify the expression:
$PAR
\( ($num1 $var[0]^{$n} )($num2 $var[0]^{$m}) \) =  \{ ans_rule(20) \}
END_TEXT

######################################
#  Answers
# Format the answer so that it shows up correctly
# in the "Correct Answer" box, i.e. put the variables
# with negative exponents in the denominator.
# NOTE: If more variables are used, just put 
# the exponents in the @expos vector in order.

Context()->operators->set(@LimitedPowers::OnlyPositiveIntegers);

$numerator = $num1*$num2;       #Constants
$denominator = 1;
@expos = ($n+$m);

$ans = SimplifyExponents($numerator,$denominator,~~@var,@expos);

ANS($ans->cmp->withPostFilter(AnswerHints(
   sub {
       my ($correct,$student,$ah) = @_;
       ##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 $ah->{score}==1 && $CorrectVariableNumber<$StudentVariableNumber;
       } => ["Simplify your answer.", 
             checkCorrect => 1, 
             score => 0]
)));

$showPartialCorrectAnswers = 1;

######################################


;
ENDDOCUMENT();