Exponent Properties

[kevinh]

It seems to me that exponent properties are taught in 8th grade with numerical bases, and I can’t tell which standard in Algebra 1 is the first to cover exponent properties with variables as the bases, like (2x^3)/(4xy^-2). Can you tell me where that change occurs?

I teach in a non-CCSS state (VA), but I’m trying to correlate my lessons to CCSS over the summer so I can share them on the web.

[Bill McCallum]

Once students start using letters to stand for numbers in a systematic way, anything they can do with numbers they can also do with letters standing for numbers. The exponent rules are important in all sorts of situations, for example working working with exponential functions (A-SSE.3c) and with polynomials and rational functions (A-APR). The sort of problem you mention here strikes me as more a sort of algebraic calisthenics—not directly required by the standards, but possibly useful in generating fluency with algebraic manipulations. I would use them sparingly, however; it is possible to go overboard with this sort of thing. And it’s not obvious to me that a student who has done plenty of these would be able to notice that, for example $e^{kt} = (e^k)^t$, which strikes me as much more important.

[kevinh]

Thanks, I do agree with you, but I don’t have a choice in giving students lots of practice on this skill. It’s a major aspect of the Virginia Standards of Learning for Algebra 1. But now I know why I can’t find it explicitly in the CCSS.

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