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 served 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 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 to lots of Y multiplied together and here we've got 3 lots of Y I'm what you'll add together 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 / y squared what do we mean by that well let me write out Y to the...

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