5.1 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 $2\left(2^x\right)=2^{x+1}$ is really just a special case of $2^a{2}^b=2^{a+b}$ , where $a=1$ .

In #3, I really want to get at the idea that $\frac{3^{\text{12}}}{3^{\text{10}}}=3^2$ , and $\frac{3^{\text{10}}}{3^{\text{12}}}=\frac{1}{3^2}$ . 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.

Homework: