In this video we'll be looking at powers and roots. So I thought I'd just make a separate video on this because it's very common within topics and it's often overlooked by a lot of teachers. So let's take the most common types of powers here. So just cubes to the power of four, squares are also a very common thing.
But all it means, so for example two cubed is two times by itself three times. So the power indicates how many of them there are. Just before I continue, pause the video, see if you can guess what 3 to the power of 4 would be.
So having a quick look at that, hopefully you've managed to give it a go. So 3 to the power of 4 would just be 3 times itself 4 times. And again, 1, 2, 3 and 4. So this is often quite common in GCSEs, you might get like a one mark question, evaluate this. So 2 times 2 times 2 is 8. 3 to the power of 4. is 81. So 3 times 3 is 9. Times by 3 again we get 27. Times that by 3, 81. That might seem quite complicated now but it's one of those things you just kind of remember it with practice. So don't worry too much if it's a bit confusing at the moment.
Okay so roots on the other hand are the exact opposite. So let's take the square root of 16. So there is a number that times is by itself. So something times by something where they are the same number.
to make 16. Now this is quite an obvious answer because 16 is quite a small number so it's quite common but this would be 4 times 4 so the square root of 16 is simply 4. Now let's take a look at something slightly harder so rather than the square root how about the cube root so again all that means this 3 indicates that that number has now been repeated three times so there is one number that exists that times by itself together three times to get to 27. And again it's one of those things trial and error or with practice you'll learn it, but 3 times 3 times 3 is going to make 27. So the cube root of 27 is 3. Now when it comes to these, because the numbers can get quite high quite quickly, for example 5 to the power of 4 is 5 times 5 times 5 times 5. Now, we get 25. Times by 5 again is 125. Times by 5 again is 625. And again, with practice, that will become more obvious. But you will very rarely be asked to do anything more than to the power of 4 or something. So anything over like a thousand of an answer is not going to be realistic.
You're not going to be expected to know that. So the highest number you will get is something like this I think. So don't worry too much about that.
Anyway I hope that was helpful and thank you for watching.