My 8th-grade son is practicing exponent

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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:
1. **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)
2. **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?
3. **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.