CK-12 Basic Algebra, Volume 2 Of 2

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Well this right here is a to the third times itself four times. So this is equal to a to the third times a to the third times a to the third times a to the third. Well, we have the same base, so we can add the exponents. So there's going to be a to the 3 times 4, right?

This is equal to a to the 3 plus 3 plus 3 plus 3 power, which is the same thing is a the 3 times 4 power or a to the 12th power. So just to review the properties we've learned so far in this video, besides just a review of what an exponent is, if I have x to the a power times x to the b power, this is going to be equal to x to the a plus b power.

We saw that right here. We also saw that if I have x times y to the a power, this is the same thing is x to the a power times y to the a power. We saw that early on in this video. We saw that over here. That's what this is saying right here. And then the last property, which we just stumbled upon is, if you have x to the a and then you raise that to the bth power, that's equal to x to the a times b.

And we saw that right there. So let's use these properties to do a handful of more complex problems. Let's say we have 2xy squared times negative x squared y squared times three x squared y squared. And we wanted to simplify this. This you can view as negative 1 times x squared times y squared. So if we take this whole thing to the squared power, this is like raising each of these to the second power. So this part right here could be simplified as negative 1 squared times x squared squared, times y squared. And then if we were to simplify that, negative 1 squared is just 1, x squared squared-- remember you can just multiply the exponents-- so that's going to be x to the fourth y squared.

That's what this middle part simplifies to. And let's see if we can merge it with the other parts. The other parts, just to remember, were 2 xy squared, and then 3x squared y squared. Well now we're just going ahead and just straight up multiplying everything. And we learned in multiplication that it doesn't matter which order you multiply things in.

So I can just rearrange. We're just going and multiplying 2 times x times y squared times x to the fourth times y squared times 3 times x squared times y squared. So I can rearrange this, and I will rearrange it so that it's in a way that's easy to simplify.

CK-12 Basic Algebra, Volume 2

So I can multiply 2 times 3, and then I can worry about the x terms. Let me do it in this color. Then I have times x times x to the fourth times x squared. And then I have to worry about the y terms, times y squared times another y squared times another y squared. And now what are these equal to? Well, 2 times 3. You knew how to do that. That's equal to 6. And what is x times x to the fourth times x squared.

Well, one thing to remember is x is the same thing as x to the first power. Anything to the first power is just that number. So you know, 2 to the first power is just 2. So what is this going to be equal to? This is going to be equal to-- we have the same base, x. We can add the exponents, x to the 1 plus 4 plus 2 power, and I'll add it in the next step. And then on the y's, this is times y to the 2 plus 2 plus 2 power. And what does that give us? That gives us 6 x to the seventh power, y to the sixth power.

And I'll just leave you with some thing that you might already know, but it's pretty interesting.

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And that's the question of what happens when you take something to the zeroth power? So if I say 7 to the zeroth power, What does that equal? And I'll tell you right now-- and this might seem very counterintuitive-- this is equal to 1, or 1 to the zeroth power is also equal to 1. Anything that the zeroth power, any non-zero number to the zero power is going to be equal to 1. There was a problem filtering reviews right now.

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Kindle Edition Verified Purchase. It would be a lot better if I had volume 1, too, but it doesn't seem to exist It seems to me that volume 2 is incomplete without volume one and since I'm home schooling my child and do not want his education to be incomplete, I'd sure like volume one I do not recall ever taking Algebra in High School or College so there is no time like now to start and I am a big believer in improving oneself. And since it is free why not a person has nothing to lose and everything to gain so enjoy the freebie in life. I downloaded this to use as a primer to brush up on my algebra skills.

I had not even completed the first chapter when I realized I was correcting errors in the printed mathematics.

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I was not impressed, but I got what I paid for with a free download. Algebra is really hard to learn and this book will help you understand the algebra equations and answers. We all need to learn math.

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Easy to use and visually very good on the iPad2. Written very clearly, good examples, but I would definitely recommend "Math Better Explained" to compliment teaching algebra. One person found this helpful. Great book I was very pleased to add this to my Kindle collection. It is very helpful and I have learned much.

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