Hi, my name is Claire Gallaher and I am the author of "Master Whacky Way," which is the GCSE maths textbook designed to help students with their GCSE maths. Today, I am here to discuss indices and make them a bit more fun and interactive. When dealing with indices that have unknowns such as X or Y, it's all about bringing them together and simplifying them. Let's start with an example: Y to the power of 4 times Y to the power of 5. Since both Y's have the same base, we can simplify them together. If we had different bases like Y and X, we wouldn't be able to simplify them. However, since we have two Y's, we can use a rule that brings them together nicely. To simplify, we need to look at the multiplication sign. The numbers 4 and 5 are up in the air, so the multiplication sign needs to go up as well. As it leaves the ground, it twists and becomes a positive. Therefore, the X will become an addition sign, and we can add 4 and 5 together to get Y to the power of 9. It's as simple as that! Let's try another example: Y to the power of 7 times Y. You might think we can just add them together, but we have to be careful. When Y is on its own, it is actually Y to the power of 1, not Y to the power of 7. If Y to the power of 7 was there, it would simply be 1. So, we have Y to the power of 1 plus Y to the power of 7, which gives us Y to the power of 8. Now, let's bring in some more numbers. In the next example, we have 3T to the power of...