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### Instructions and Help about Why Form 5495 Index

Hi my name is Claire Gallaher on the author of Master whacky way which is the GCSE maths textbook to help students with their GCSE maths now I'm here today to run through indices to make them a bit more wacky and indices where we have some unknowns so you might see an X you might see a Y it's all about bringing them together and simplifying them let's take for example Y to the power of 4 times y to the power of 5 now because they're both Y's what we're able to do is actually simplify it together now if they were different if we had a Y and X we wouldn't be able to simplify them because they're two y's we can use a rule which will just bring them together nicely what we're going to do is we're going to look at the multiplication sign and this needs to be up in the air because the numbers four and five are up in the air now the multiplication sign is down here we need to take it up and because it leaves the ground it's windy and it twists and becomes a positive so the x is going to leave the ground go up to join the numbers and will become an addition sign that will therefore mean that we add the 4 and the 5 together which gives us Y to the power of 9 it's as simple as that let's take another one so if we have a look at Y to the power of 7 times y what you might think with this one is well let's take the multiplication sign up into the air it will twist and become a plus let's add them together well there's a 7 but there's nothing else there what we have to be careful of is Y on its own is actually Y to the power of 1 it's not Y to the power of because then it wouldn't be there that would just be 1 so Y on its own is Y to the power of 1 7 plus 1 gives you 8 so we're doing exactly what we did before the multiplication sign is going up in the air it's becoming a positive and that therefore gives us Y to the power of 8 now hopefully we're okay with that so let's bring in some more numbers if we have a look at the next example we've got 3 T to the power of 5 times 42 the power of six now in this example we've got two levels we've got a level where the multiplication sign is but we've also got another level up where the powers are now the multiplication sign where there's numbers on that level we will use that sign we will multiply however like we've been doing before where we need it to go up in the air to join the other numbers that again is windy will go up twist and become an addition so we have the three times the four which will give us the twelve then we have the five plus the six which gives us the eleven bring it all together we have twelve T to the power of 11 let's just try one more of those so the next example we have is 6m to the power of five x 9m now we've got the same issue here in that we've got two levels but also M is on its own and as we've seen already and M on its own is M to the power of 1 so 6 times 9 is 54 now if we don't know how to work out our 9 times tables remember one way you can do it is to use your hands if we were looking at 1 times 9 we'd put the first finger down that just leaves us with 9 now if we were looking at 2 times 9 we put the second finger down that would then leave us with 1 then a gap and 8 that gives us 18 3 times 9 again split these up two but then with my five fingers on this hand we get 27 X cetera etc so that's a good way for us to work out our 9 times tables now obviously we don't have 12 fingers we can only do it up to 10 times 9 you just need to remember 11 times 9 which is of course 99 and 12 times 9 which is 108 so 6 times 9 on our fingers 6 finger down 5 and 4 54 5 up in the air and the one up in the air we take the multiplication sign up it becomes a plus when it's windy and twists so that gives us 54 m to the power of 6 now so far we've only looked at multiplication let's have a look at division similar rules here so if we had p9 divided by p2 where we have a division sign down here on this level is going to go up in the air and it's windy so what's going to happen it's going to lose its dots so what was it divided down here will become a subtract up here so we have P 9 divided by p2 well that's going to give us p7 because of course we end up with 9 take away 2 up the top there let's just run through another one see 8 divided by C 3 again same issue we've got the divide that goes up in the air and loses its dots we end up with C 5 now we can also make these ones a bit tougher by introducing the numbers in front of the unknowns just like before it's all about levels so if we have 24 W to the power of 12 divided by 6 W to the power of 7 we're going to.

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