Lesson goal: Combining exponents

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One of the coolest advances of doing math on the computer, is the computer's ability to do symbolic math. This means the computer can do algebra, which means properly handling the math for all of the $x$'s, $y$'s, and $z$'s (you know, "the symbols").

We've developed a function called algebra that actually knows how to "do algebra" on a mathematical expression you give it.

Let's start with some basic algebra here, which involves combining exponents, when a bunch of variables are raised to some power. You've probably seen problems like this before, ones that call for "simplifying expressions" like: $x^2x^5$ or $z^3x^2z^{-1}$.

Try these first, and then try some of your own homework problems!
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Now you try. Try programming in some expressions, like $xy^2y^{1/3}$, $zxyyzxz$ or $\frac{1}{2}x^{3/2}y^2x$, to see how the exponents come out.

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