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Hi there and welcome to another video from Hegarty maths it's mr. Haggerty here and in this video we're talking about index form our first video on the topic where we introduce the ideas and we talk about in particular powers of positive integers so to start with if someone said - - - - - - - added but to itself six times mathematicians have a way of writing that they would say that is six multiplied by two or six lots of - right now I want you to consider just in the same way that this is six lots of - imagine instead of a repeated addition I had a repeated multiplication like 2 times 2 times 2 times 2 times 2 times 2 2 times by itself 6 times a mathematician is bound to have a quick way of writing it do you know how they do it well they write - like this to the power of 6 and that means the number 2 is multiplied by itself 6 times and that's their shorthand way of doing it because after all they are fairly lazy so let's expand on this idea do times 2 times 2 times 2 times 2 times 2 a mathematician would write 2 with a little number there 6 and the way they would say it they would say 2 to the power of 6 now the number 2 has a special name this is called the base number it is the number getting multiplied by itself and the 6 here has some different names actually it may be called the index okay it may be called the power and sometimes it's even called the exponent and all of those things are just how many times the base number gets multiplied by itself ok now just a little bit more vocabulary when you see let's say a number 7 to the power of 2 let's say so 7 x 7 mathematicians say that as 7 squared they have a way of saying that one that's an unusual one and if you had 7 to the power of 3 they usually say that as 7 cubed but anything with a 4 5 6 or 7 as powers they say 7 to the power of 4 7 to the power of 5 etc so it's only worth just noting because you will hear them from your teachers and see them in textbooks right there you go that's index notation so simple so I want us to fill in some tables of index notation just to get the feel and the flavor for what they look like and start spotting some patterns that's going to help us later on imagine I gave you two cubed or two to the power of three what does it mean well it means 2 times 2 times 2 which is 8 the next one what do you think the one below I'm going to give you that's right two squared that means 2 times 2 and the answer is 4 now look what's happening here as I'm going down I'm reducing the exponent of the power by 1 I'm getting one less 2 in my multiplication and I'm having my answers are 9 8 divided by 2 gives me 4 so what do you think the next one is going to be well it's going to be 2 to the power of 1 which will be 1 2 multiplied by itself and 4 divided by 2 as I go down as clearly - what do you think the next one's going to be 2 to the power walk that's right 0 now it's going to be the answer 1 and why because as we were going down we said we were dividing by 2 all right and 2 divided by 2 is 1 so 2 to the power of 0 has to be 1 there's nothing else it can be if the patterns working now here's where it gets tricky the next one is going to be 2 to the power walk negative 1 that's right and because we're dividing by 2 each time 1 divided by 2 is 1 over to 1/2 and what do you think 2 to the negative 2 is going to be can you spot that well it's going to be 1 over 2 times 2 okay you're going to divide by an extra 2 you can have an or think of it as you're going to have an extra 2 multiplying on the denominator so you're going to get 1/4 and can you imagine what the last ones going to be 2 to the negative 3 it's going to have three twos multiplying together on the denominator and the answer will be 1/8 and that's almost all the rules on index form okay for the remaining videos coming up so I just want you look at that and see if you can study the patterns on that note then could you take a second pause the video and fill in the meaning column so for example in this case I want you to write 3 x 3 x 3 and then the answer which would be 27 see if you could fill it in for the other powers did you get the following hopefully you did I can't encourage you enough to try doing these because the minute you start doing them and you spot what's going on in the pattern you're learning so many of indices rules that are coming up in their forthcoming videos try another one can you fill that in pause the video do have a go well hopefully you got the following ok and if you did do the video you are really starting to spot the patterns here so let's do one more could we feel all that grid in hopefully you got the following and the last one powers of 10 really important could

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