Me Or My Maths: And Negative Powers

Me Or My Maths: And Negative Powers.: ". . . Hence, (a) [the multiplication cancellation laws] then tell us that no matter what a is, a^0 = 1 ."

My students are always asking me why this is true (they just won't accept the pattern of 10^2=100, 10^1=10 and 10^0=1). Beans also shows us why a^-k = 1/a^k. It won't take long to show students (in college, not 7th grade!) this. Maybe, on second thought, 7th graders would get it.

By the way, I found the above mentioned exponent post on Me Or My Maths because of  How Many Frenchmen Can’t Be Wrong?: Vlorbik on Math Ed.

≤≥ ≤≥ ≤≥ ≤≥ ≤≥ ≤≥

I have two ways to solve Dave Marain's challenge (see previous post) and have not had even one minute to do the third way. I may do it tonight because I suddenly have time because I never made it to a meeting tonight. Dave specifically prohibited two of my ways, but they are methods my middle school students would use. My third way, I hope, will be more "grown-up."

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