What Form 8655 Index 2024

Hi there and welcome to another video from Hegarty Maths. It's Mr. Haggerty here. This is our seventh video on index form and we're talking about unit fraction powers. Now, just a little warning, you must have watched all the previous videos on index form to do this one because we're combining a lot of rules. You must also have watched the square and square root videos so you're fully aware of those. Previously on Hegarty Maths, I asked you on the power of the power video to be able to work this out, and you did. You would have said that 2 to the half, all squared, is 2 to the 1/2 times 2, which is simply 2 to the 1, which is 2. You would have said that 7 cubed is equal to 7 to the 1/3 times 3, which is 7 to the 1, and the answer would be 7. We did that in the power of the power video right at the end. Now, I haven't told you what 2 to the 1/2 means or 7 to the 3rd even means, but assuming they exist, you can multiply the powers and you'll get 2. Let's think about what they must mean just from this. If we know this is true from our power of the power videos, let's think about what it means. Now, 2 to the half is something. Let's say we don't know what it is, but when you square it, you get 2. So let's think about that something when you square it, you get 2. What must the thing be? Well, it must be the square root of 2, mustn't it? It must be the square root of 2 because the only thing that multiplies by itself to get 2 is the square root of...