I get very upset when I hear students regurgitate rules for mathematical properties, but have no sense of why the rule exists. To be quite honest with you, it wasn’t until my second year of math education courses that I understood why a negative exponent essentially had the base and the positive version of the exponent end up in the denominator of a fraction. When I came across a negative exponent in the denominator of a fraction, I was quite befuddled. I essentially made up a new rule, when it’s negative in the “bottom”, I must take to the “top”. Yeah, that fixes everything, right? Not quite. Students are forever making up rules as they go along, adding to and modifying what they have been told in the past, creating bandaids of sorts to get them through to the next round. How about we step back and give a logical reason for things, so students build upon and apply knowledge, instead of inventing their own.
Please take a look at this short piece that explains the effects of taking a base to a negative exponent. Every student needs to understand this reason.