Topic: Fractional (Rational) Exponents
Today’s active learning was on extending our work on exponents to include rational exponents. We started out by reviewing how to simplify square roots. Here are the problems:
Simplify, assuming that $x$ and $y$ are both $\ge 0$. [Why do we need to assume this? What difference does it make?]
(1) $\sqrt{9x^{2}}$
(2) $\sqrt{128}$
(3) *Sorry, I’ve forgotten exactly what I wrote for this problem. Can anyone tell us what it was?
(4) $\sqrt{x^{4}y^{9}}$
The active learning problems are here:
MAT1275-F15-Shaver.sshaver.RootsRadicalsShort
For these we used the definition of the fractional (rational) exponents, together with all the previous definitions and properties of exponents. All of the properties continue to work even with rational exponents, as long as we are careful about when the radicand needs to be $\ge 0$.
Homework homework yes you have homework!
Recommended order for the WeBWorK:
• First complete the assignments that are due tonight, obviously.
• Then complete the assignments HigherRootsAlgebraic, RationalExponents, and FrractionalEquations, if you have not already done so.
• At the same time you are working on those assignments, start working the Test3Review a few problems at a time. It’s best to schedule time on at least 3 of the 4 days before the Test (including today) and not try to do all the Test Review at once.
Here are some typed notes and a summary of the definitions and properties of exponents, which may be helpful:
MAT1275coExponentsDefinitionsLaws-Condensed
A more comprehensive post on reviewing for Test 3 will go up soon, but until then, see the Test 2 Review post, which contains much of the same advice.
