Hello and welcome to a lesson on the rules of indices. This lesson will be equally applicable to higher-tier GCSE and to the early modules available. What I'm going to do is deduce the eight rules of indices by looking at examples in algebra. Then, once I've got all the air rules of indices, we look at a further ten examples to put them into practice. So, let's begin. Let's first begin by considering y squared multiplied by y cubed. What does that actually mean? Well, y squared is y times y, and y cubed means y times y times y. So, if we multiply those together, the brackets actually serve a more useful purpose. We can just remove the brackets. So, we've got y times y times y times y times y. But that is exactly what we mean by y to the power 5. So, y squared multiplied by y cubed means y to the power 5. Now, that leads us to our first rule. A more general rule is if we've got x to the power p multiplied by x to the power q, then what that's going to give us is x to the power p plus q. Because if we've got two lots of y multiplied together, and here we've got three lots of y, when you add them all together, we end up with 2 plus 3 lots of y. So, more generally, if we have p lots of x multiplied together q lots of x multiplied together, then all together we'll have p plus q lots of x multiplied together. Moving on now to find a second rule for indices, let's consider y to the power 5 divided by y squared. What do we mean by that? Well, let me write out y to...
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