Simplify an expression using rules of exponents when the denominator has negative exponent 

Great video. Some of your students were lost that a NEGATIVE power in the denominator, can be moved, with its components, to the numerator and become a POSTIVE power in that process. You gave an example why, but it was too fast to soak in (to keep within time constraints you have to be, but the students need to be given an overnight reinforcement exercise on that to instill the how and why into their minds - any doubts and any further learning processes breaks down for them - as it is happening here from the past). Then some also seemed to be missing the point that once all the terms (between any additions, subtractions, or none at all) are now ALL products (multiplies), they can now be rearranged any way you want (within the Adds and Subtracts if any). You gave an example on that too, but some were not making the connection from the example to the problem. I teach Summer STEM and I may have to teach SOME math skills to 3rd graders along with say 9th graders - that is really hard to do. But even if all my students are in the same grade and all exposed to the same math techniques, each have their own levels of understanding (Swiss Cheese so to speak) so even that is hard to overcome for a teacher. Sadly if we could give each student 4 hours of math teaching on their own every day, and then an hour as a group once everyone has the new concept locked, that would be great, but not very practical. About 20% students have Swiss Cheese knowledge/retention of the math to their current level, and should seek dedicated nightly tutors. If a student does not grasp or forgets even one technique in Algrebra and higher math, they will struggle to achieve good grades or be good at math the further along they go - there is LOT to retain. I wish I could develop a math program from Kindergarten to college Graduate where each student is evaluated daily and only moves to the next topic only after proving the new topic is understood and all prior topics are proved to be retained. If not, the student stays at that class step or goes back if needed. Can you imagine? Each student would end up in their own individual class and moved forward (and backwards) at various rates - overall learning may be much slower but more effective - but not practical at all in general. So, I my opinion, math would be optimumally taught one-on-one, with too much time at one topic requiring an "abort" to learning any more math. Harsh, but it would be better rather than indidivual disjointed courses designed for groups using the average math learning curves (not everyone fits and some may never).

thank you, this helped a lot!

I think the problem your students are trying to understand is the fact that your multiplying the base numbers in this video of exponents rather then finding a common denominator and dividing like you did in the other video, where you simplified multiple properties of exponents.

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I was a little confused about not using the distributive property with the 3(x to the 6, y to the 3), even though he said everything multiplies, so you don't need to distribute. Then I recalled, The Distributive Property is easy, because "multiplication distributes over addition" There is no addition in the parentheses so, nothing to distribute over. So, for me, If I am going to be able to do the math, I need to understand ALL the details, all the time.

6th

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didn’t help