# Tag Info

### How should I convince a student who thinks they proved $1=-1$

Should we impose that $(a^m)^n=a^{mn}$ only when $a \gt 0$? Maybe you should tell your student that he/she have discovered by himself/herself the proof that the rule $(a^m)^n=a^{mn}$ cannot be true ...
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Rigid criteria for simplification seem to me largely a bad idea if they are not motivated by contextual considerations. The idea that $\sqrt{2}/2$ should be preferred to $1/\sqrt{2}$ struck me as ...
• 5,869

### How should I convince a student who thinks they proved $1=-1$

Obviously the correct mathematical answer is to show how the exponent rules actually work, and when they do not work. So please don't accept this answer. Anyway, the educational answer is to see ...
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### How should I convince a student who thinks they proved $1=-1$

When I asked the What are the Laws of Rational Exponents? question on SE Mathematics, I was largely thinking about this context; teaching at the level of high school or early (remedial) college math. ...
• 26.3k