I'm working on a problem using some physics equations, and in one part I asked the student to solve a system of two equations for one of the variables in terms of the other variables. I simplified my answer a little bit when writing the answers so that it would be clear and easy to read when being presented to the user, but when I tried it out, an equivalent formula was not accepted as correct. I haven't had this problem before, but is there something I'm doing wrong or a way around this problem? I'm afraid that this sort of problem applies to many formula answers, and that the comparator is rejecting input equivalent to the answers.

Here's a snippet of the code:

------------------------------------------------------------------------------

...

Context("Numeric");

Context()->variables->are(G => 'Real',

M => 'Real',

R => 'Real',

v => 'Real',

a => 'Real',);

...

Context()->normalStrings;

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

##ANSWERS SET 2##################################################

$ans1 = Compute("sqrt(G M /a)");

$ans2 = Compute("(a G M)^(1/4)");

$ans3 = NumberWithUnits("sqrt($Gwithout *$Mwithout /$awithout) m");

$ans4 = NumberWithUnits("($awithout *$Gwithout* $Mwithout)^(1/4) m/s");

ANS($ans1->cmp());

ANS($ans2->cmp());

ANS($ans3->cmp());

ANS($ans4->cmp());

...

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There's part of a screenshot in the attachment.

I typed sqrt(a*sqrt(G M /a)) as input for the record, but sqrt(sqrt(a G M)) works as well as (a G M)^(1/4).

Again, thank you for any help.