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"ExponentiationResult" (Comparison Method)

"ExponentiationResult" (Comparison Method)

This function has not been fully integrated into the long-term Mathematica system, and is subject to change.
Compare mathematical expressions in a way suitable for exercises about powers, square roots, and radicals allowing only computation that does not include operations of exponentiation.

Details

  • The exponentiation result comparison method considers two mathematical expressions to be equivalent if they do not differ by any exponentiation operations, e.g. x*xx^2
  • Answers are considered correct even when containing differences that are not exponentiation operations, such as basic arithmetic or factoring of numeric coefficients.
  • The values of the key and answer can both be specified as held expressions Hold[expr] to maintain the values exactly as they were given. Even when the values are held, evaluation of non-exponentiation functions (i.e. excluding Power and Sqrt) are performed within the held values during assessment. It is recommended to always hold the answer.
  • The following tables show comparisons of "ExponentiationResult" with other comparison methods for typical answer keys:

Examples

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Basic Examples  (3)

Create an AssessmentFunction for a power question:

Wolfram Language code: af = AssessmentFunction[Hold[2Sqrt[7]], "ExponentiationResult"]

Use it to assess answers:

Wolfram Language code: af[Hold[Sqrt[28]]]
Wolfram Language code: af[Hold[Sqrt[7]2]]

Create an assessment with for an algebraic expression containing radicals:

Wolfram Language code: af = AssessmentFunction[Hold[2Sqrt[3] + 2x], "ExponentiationResult"]

Only factored expressions which are not involving exponentiation when expanded are considered correct:

Terms like integers which do not include square roots or exponents can be factored within correct answers:

Wolfram Language code: af[Hold[2(Sqrt[3] + x)]]

Factoring terms with square roots creates an incorrect answer:

Wolfram Language code: af[Hold[Sqrt[2](Sqrt[6] + Sqrt[2]x)]]

Create an assessment for a question about exponents:

Wolfram Language code: af = AssessmentFunction[Hold[2x ^ 3 + x], "ExponentiationResult"]

Answers differing by factoring of numerics are considered correct:

Wolfram Language code: af[Hold[2(x ^ 3 + x / 2)]]

Answers with different representations of the exponents are considered incorrect:

Wolfram Language code: af[Hold[2x(x ^ 2 + 1 / 2)]]

Scope  (2)

Create an assessment function for the solution to x^3*x^2*y^2:

Wolfram Language code: af = AssessmentFunction[Hold[x ^ 5 * y ^ 2], "ExponentiationResult"]

The original question is not accepted as an answer:

Wolfram Language code: af[Hold[x ^ 3 * x ^ 2 * y ^ 2]]

Equivalent mathematical expressions that are invariant in exponentiation are considered correct:

Wolfram Language code: af[Hold[y ^ 2 * x ^ 5]]
Wolfram Language code: af[Hold[y ^ 2 * x ^ (3 + 2)]]

Create a QuestionObject for a square root problem:

Wolfram Language code: QuestionObject[ QuestionInterface["ShortAnswer", <|"Prompt" -> StringForm["Simplify the expression ``", HoldForm[Sqrt[20] + Sqrt[80]]], FieldHint -> "Find a common factor"|>], AssessmentFunction[Hold[6 Sqrt[5]], "ExponentiationResult"] ]