x³·x⁴ vs (x³)⁴: add or multiply the exponents?
x³ · x⁴ = x¹² and (x³)⁴ = x⁷ are both wrong, both common, and both always in the answer choices.
Why it happens
Two similar-looking rules stored side by side interfere with each other. Without a quick derivation habit, retrieval is a coin flip.
See the trap
Simplify x³ · x⁴ and (x³)⁴.
x³·x⁴ = x¹²; (x³)⁴ = x⁷.
x³·x⁴ = x³⁺⁴ = x⁷; (x³)⁴ = x³ˣ⁴ = x¹².
How to actually fix it
- 1Forget the rule? Expand: x³·x⁴ = (xxx)(xxxx) — count 7.
- 2Multiplying same bases → add exponents; raising a power → multiply.
- 3Rebuild the rule from a 2-second expansion instead of guessing.
Practice this trap · 1 real question
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
What about (2x)³?
The exponent hits every factor: (2x)³ = 8x³. Leaving the 2 unraised is its own classic distractor.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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