Why Form 2220 Index 2023-2024

Hi there and welcome to another video from Haiti Mats. It's Mr. Haggerty here, and in this video, we're talking about index form again in our sixth video. But this time, we're talking about powers of powers. And I'll explain what I mean. Now, before we get going, what does 49 to the power of 4 mean? Well, hopefully, you know that it means the following: 49 x 49 x 49 x 49, right? We know that. Now, here's the news-style question: What does 7 squared, which, by the way, is 49 (I picked that number on purpose), to the power of 4 mean? Well, it must mean 7 squared x 7 squared x 7 squared x 7 squared, right? It's got to mean that. If 49 to the power of 4 means 49 multiplied by itself 4 times, 7 squared to the power of 4 must mean 7 squared multiplied by itself 4 times. But what does 7 squared actually mean? What this means is 7 times 7, right? And what does this one mean? 7 times 7. And this one? 7 times 7. And this one? 7 times 7. And we're multiplying the 7 squares by each other, repeated in there. Now, how many 7s do we have multiplying together? One, two, three, four, five, six, seven, eight. This is going to be therefore written as 7 to the power of eight. Now, can you spot what I'm trying to show you here? I've shown you that 7 squared to the power of 4 is the same thing as 7 to the power of 8. What am I trying to show you? Well, if you are doing a power raised to another power, so 7 squared to the power of all of that raised to another power, the...