I see all the time in high school math textbooks problems saying to "simplify" an expression. Their explanations of what it means for an expression to be "simplified" is a bit vague and does not reflect the rigor mathematics usually provides:
"To simplify an expression means to do all the math possible." (OpenStax Intermediate Algebra)
I have encountered numerous situations in which there is ambiguity as to what looks "simpler" to people. For example: $$ \text{Simplify: }\frac{a^2b^{-3}c}{c^2b} $$
Some people would say the most "simple" way to write this is $a^2b^{-4}c^{-1}$. However, most textbooks would consider $\frac{a^2}{cb^4}$ to be the "correct" answer.
From my perspective, problems beginning with "Simplify" don't really make sense (and are frankly unfair to the students) unless there is a clear definition of what it means for the expression to be "simplified" (especially with teachers who are picky about that kind of thing).
Is there some sort of convention for simplification that I don't know about that makes this work?
from Hot Weekly Questions - Mathematics Stack Exchange
Caleb H.
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