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.

NegativeExponents

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Check out the file below for instructional notes for teaching the multiplication of monomials. These notes include the multiplication of like bases, the application of scientific notation and the concept of a power raised to a power. These notes are designed to enhance the understanding of the algebraic rules students often times confuse. The central theme should be to emphasize the meaning of a power over and over with students instead of restating algebraic versions of rules. I hope this helps.

MultiplyingMonomials

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