STEM AND ASSESSMENT EVIDENCE WORKBENCH
Compare learner exponents with exact same-base product, quotient, and power-of-a-power laws, including zero and negative cases.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
For nonzero base x, x^a times x^b equals x^(a+b), x^a divided by x^b equals x^(a-b), and (x^a)^b equals x^(ab). These identities extend to integer exponents under their domain conditions. The engine calculates only the expected resulting exponent and compares it exactly with the learner integer. A supported claim applies the declared law to the two entered exponents. A diagnostic can identify a visible rule substitution, such as adding during a power of a power, but it cannot establish the learner thought process. Ask for an expansion, reciprocal explanation, or numerical counterexample and then check coefficients, signs, bases, and parentheses in the complete expression.
Confirm the prompt, approved source, units, symbols, notation, expected model, and review threshold. Keep an unchanged copy of observations or learner responses before editing any row.
Run the worked example, inspect intermediate rows, and compare the evidence with a hand calculation, diagram, physical model, periodic table, or moderated assessment source.
Record the method, assumptions, units, classifications, rounding, and flagged rows. Treat the downloaded report as editable evidence and verify it independently before instruction or assessment.
How to interpret the result
Use after learners simplify symbolic exponent expressions and the resulting exponent is the evidence of interest. The diagnostic separates three commonly confused laws and highlights specific add-versus-multiply patterns. It does not simplify coefficients, combine different bases, determine domains, evaluate zero-base edge cases, process sums, distribute powers across full expressions, or verify an entire algebraic solution.
The product x cubed times x to the fourth gives exponent seven. The quotient with exponents eight and three gives five. A power of a power with exponents two and five gives ten. A negative product exponent combines correctly to three. The final power-of-a-power response adds three and four to get seven and is flagged because those exponents must multiply.
For nonzero base x, x^a times x^b equals x^(a+b), x^a divided by x^b equals x^(a-b), and (x^a)^b equals x^(ab). These identities extend to integer exponents under their domain conditions. The engine calculates only the expected resulting exponent and compares it exactly with the learner integer.
A supported claim applies the declared law to the two entered exponents. A diagnostic can identify a visible rule substitution, such as adding during a power of a power, but it cannot establish the learner thought process. Ask for an expansion, reciprocal explanation, or numerical counterexample and then check coefficients, signs, bases, and parentheses in the complete expression.
Do not multiply exponents in a same-base product, add them in a power of a power, forget to subtract the entire denominator exponent, combine unlike bases, or interpret a negative exponent as a negative value. Keep parentheses visible, state nonzero-base restrictions for division and negative powers, and avoid applying product rules across addition.
Learning boundary
This browser-local workbench applies only the disclosed model to entered values. It cannot diagnose a learner, certify an experiment, establish a chemical fact, classify a task automatically, or replace teacher and laboratory judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid names and other personal information, and retain authoritative records only in the system approved by the school.
No. It reports how the entered evidence behaves under one disclosed rule. Ask for reasoning and compare several evidence sources before reaching an educational conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, use the course method, and follow the applicable academic-integrity rules.
YOUR NIRMION
