My 8th-grade son is practicing exponent
提问
My 8th-grade son is practicing exponent rules and polynomial operations in algebra. On his quiz yesterday, he got this question marked wrong:
"Simplify: (2x^3)^4"
He wrote down:
(2x^3)^4 = 2x^12
When I asked him how he got it, he explained: "Power of a power means you multiply exponents, so 3 times 4 is 12, and the 2 just stays in front!"
He completely missed that the entire term inside the parentheses is being raised to the 4th power, meaning the coefficient 2 must also be raised to the 4th power: 2^4 = 16, giving the correct answer of 16x^12.
Could you help us format this into our mistake notebook:
- Strict 5-Line Mistake Card: Please format this into the exact standard 5-line card format:
- 题面 (Problem statement)
- 错法 (The incorrect step he took)
- 修法 (The correct mathematical remediation)
- tag (Classification tags)
- 错因 (Cognitive root cause analysis)
- First-Principles Parent Demonstration: How can I write this out for him on paper as repeated multiplication (e.g. writing out (2x^3) four times in a row) so he visually grasps why the 2 multiplies by itself four times?
- Parallel Practice Redo: Provide one changed-number parallel problem for tonight (e.g. (3a^2)^3) without providing the final answer key to the student.
回答
I need to check the family profile for timezone and read the capture reference for the card structure.
The "first-principles" demonstration and the rule behind it belong with homework-tutor — that's the teaching/explaining side, not the notebook.
The card itself only holds five lines — prompt, wrong move, repair (one same-type item), tag, cause — no rule explanations on it.
Prompt (题面):
Wrong move (错法):
Repair (修法):
Tag:
Cause (错因):