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Rules of Exponents

Module by: Kenny M. Felder. E-mail the author

Summary: A teacher's guide to the rules of exponents.

Yes, a lot of this assignment was already done, verbatim, in the unit on Functions. But there are a lot of reasons for bringing it back (just as we did in Quadratics). First, they (and you) can discover that they have gotten better at finding generalizations. But more importantly, back when we did this in functions, we were only interested in the process of finding generalizations. Now we are focused on creating, memorizing, and using the three rules of exponents.

2d is really pushing them another step toward “the way mathematicians think”—seeing that 2 ( 2 x ) = 2 x + 1 2( 2 x )= 2 x + 1 is really just a special case of 2 a 2 b = 2 a + b 2 a 2 b = 2 a + b , where a = 1 a=1.

In #3, I really want to get at the idea that 312310= 3 2 312310 size 12{ { {3 rSup { size 8{"12"} } } over {3 rSup { size 8{"10"} } } } } {}= 3 2 , and 310312= 132310312 size 12{ { {3 rSup { size 8{"10"} } } over {3 rSup { size 8{"12"} } } } } {}=132 size 12{ { {1} over {3 rSup { size 8{2} } } } } {}. In other words, the whole thing can and should be done without negative exponents. Why? Because we haven’t yet defined what they mean—and why.

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“Homework: Rules of Exponents”

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