Let us assume that the students haven’t been exposed to these two rules: ax+y=axay and axay=ax−y. They have just been introduced to the generalization: a−x=1ax from the pattern method: 22=4,21=2,20=1,2−1=12 etc. However, some students confuse 2−3 to be (−2)(−2)(−2) since they are familiar with 23=2⋅2⋅2. This is a low-income urban school and most kids in this algebra class struggle with math dealing with exponents, fractions and decimals. What would be the best approach to reach all 32 students?
You could say that the minus sign means an opposite; for instance, subtraction is the opposite of addition, and it uses the – symbol. Similarly division is the opposite of multiplication, and the division symbol has a minus sign in it (this isn’t where it comes from, but is only good for memorizing purposes).
So a minus in the exponent is the opposite of multiplying over and over again, namely dividing over and over again.