Exam-style question
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B1: A student writes (x^1/2)(x^3/2) = x^3/4. Explain the error and show the correct index law.
Model answer
What a good answer should say
- Use the product law for powers with the same base.
- When multiplying x^(1/2) by x^(3/2), the exponents are added, not multiplied, so the result is x^2.
- The error is confusing the product law with multiplication of fractions.
- Good working should name the index law, keep the base unchanged and show 1/2 + 3/2 = 2 before writing the final simplified form.
This answer is tied to the objective: B1 Understand and use the laws of indices for all rational exponents..
Explanation
Why this works
Use the explanation to connect the worked answer back to B1 Understand and use the laws of indices for all rational exponents..
This question is anchored to B1 because it tests rational exponents and the laws of indices. It rewards visible addition of exponents and a clear correction of the common misconception.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.