 Alright, today's discussion is going to be about powers and radicals, because again, these are big things that I see that students always make mistakes on. Alright, so starting with some powers, let's do how about just 3x squared, for example. Okay, so remember squaring something means that you can multiply it by itself. So I'm going to rewrite this as 3x times 3x. Okay, and then now we can multiply all the different pieces together. So that's going to give us a total of 9x squared. So when we're multiplying stuff inside the parentheses, we can distribute that square through. That's perfectly legit. Okay, but, and this is where usually students go wrong at, if we were to add these two things together, plus 3 squared, you cannot just distribute that square. Because again, remember, this means we've got to multiply x plus 3 by itself, and then we've got two sets of parentheses. So that's where you're either going to have to distribute, use a box, use everybody's favorite foil method, you know, whatever you want to do here. But we're going to end up with x squared plus 6x plus 9. Okay, so if you just square the x and just square the 3, you're going to be missing this middle term here. Okay, so squares or any kind of powers, you can distribute them if you're multiplying or if you're dividing. But if you're adding or subtracting, you're going to have to actually multiply it all out. Okay, radicals work kind of similarly. So let's say we're going to do the square root of how about 9 times 16. Okay, and I just picked perfect squares because they're fairly nice. So if we were to actually multiply 9 times 16, let me check my notes here. That gives us the square root of 144, which is again a perfect square. So that gives us a total then of 12. And if I were to break this apart, I could do the square root of 9 and the square root of 16 separately. That's perfectly legit with this one because that would give me 3 times 4, which gives me the same thing as 12. These are the same. But if we were adding or subtracting, again, this does not work. So if I were to do the square root of 9 plus 16, that gives me the square root of 25 if I were to combine those together, which simplifies down to 5. But, and this is again where students tend to go wrong at, they try to do the square root of 9 plus the square root of 16. Well, that doesn't give you 5. That gives you 3 plus 4, which is 7. These are not the same thing. Okay, so this one is the correct way to do it, obviously, because that gave us the answer that was good. But you cannot split up a square root if you're adding on the inside of it or if you're subtracting on the inside of it. You have to be able to simplify all that stuff first, then you can simplify your radical. Okay, multiplying, dividing, it is legit to split it up right away and get the same answer. But with adding and subtracting, it's not. Okay, so again, I stuck with numbers. There are fairly simple expressions here, but all these same rules apply as things get more and more complicated as you do more and more complicated radicals and powers. All right, so come back and watch this if you need to get a good refresher and then apply it to the harder problems. All right, thank you for watching.