### Video instructions and help with filling out and completing Where Form 8815 Index

**Instructions and Help about Where Form 8815 Index**

Hi there and welcome to another video from Hegarty maths if mr. Haggerty here and this is our fourth video on index form this time we're going to be talking about multiplying indices and trying to generate a rule for that so to start with I've introduced you index form how would a mathematician usually write - x - x - 7 x well they would write 2 7 1 name now I'm going to just break up this two in different ways we know that when you're multiplying multiplying is associative so I can do it in any order I want so let's just say I went like this I did that on its own and then I did those multiplied so 2 here that's 2 to the power 1 these six 2's here are 2 to the power of 6 obviously I know my answer is 2 to the 7 what if I did it in a different order what if I said right I'm going to do them to and then I'm going to do them 5 2 squared multiplied by 2 to the power of 5 is of course 2 to the seventh what if I broke it up in a different order again what if I said I don't know like this and I said right 2 to the 4 therefore multiplied by 2 to the 3 well obviously that's 2 to the 7th and I could break it up in any way I want so let's say I said I don't know I did these two and then I did these 3 and then I did these two last so that would be 2 squared multiplied by 2 cubed multiplied by 2 squared and I know the answers 2 to the 7 now can you spot what I'm trying to show you what I'm trying to show you is that when the base number is the same when you've got powers of 2 what can you do with these indices or these powers you can add them 2 to the 1 times 2 to the 6 is 2 to the 7 you can just add one at 6 2 to the 5 times 2 to the 2 is 2 to the 7 2 to the 4 times 2 to the 3 is 2 to the 7 2 to the 2 times 2 to the 3 times 2 to the power of 2 I can just add to add 3 are 2 and get 2 to the power of 7 it's numbers the same and we're multiplying powers with the same base we could just add the indices so let's just write that out so we're absolutely sure when we're multiplying indices if and only if the base numbers got to be the same when multiplying numbers in index form you can add the powers and I want to give you an example of what I mean for that so say if someone asked you to simplify or write in one index form let's say they said I don't know seven cubed multiplied by 7 to the power of five you could say well that's 7 to the three add 5 which is 8 what you're not allowed to do say if someone said 3 to the power of 5 multiplied by 2 to the power of I know 8 you're not allowed to add the powers there you're not allowed to do anything there's different bases you're not allowed to combine it you just have to leave it alone and leave it like that in fact what you really should have you should have it written with the smaller the smaller base number first that would be the mathematical way of writing that but there's no way you can actually simplify that let's say and that's it that's all you need to know for multiplying indices the base numbers the same you can add the powers let's try some questions simplify the following leaving your answer as an index form 9 to the power 5 multiplied by 9 to the power of 3 is going to be 9 to the power of 5 add 3 which is 8 8 squared multiplied by 8 to the power of 4 is going to be 8 to the 6 2 to the 4 multiplied by 2 now this is sometimes where students struggle that doesn't look like index form but remember the video where we did powers of 0 1 that's actually 2 to the power of 1 and it's really handy to be able to do that so if we add these powers we clearly get 2 to the 5 3 to the 4 times 3 to the that's right 1 times 3 to the 7 I can add 4 add 1 is 5 at 7 is 12 this will be 3 to the 12 and we're done next one pause and see if you can do right this one well we've got different bases on the go here we've got five Squared's and 5 cube but then at the same time we've got a different base which is 7 and we've got 7 cubed + 7 to the power of 6 keep them separate don't try and combine five squared multiplied by five cubed is 5 to the power of 2 plus 3 which is 5 then we're going to multiply that by 7 cubed multiplied by 7 to the power of 6 which is going to be 7 to the power of 9 okay and always write the smaller a base number first and that's it don't try and simplify that anymore that's as simple as you can get keep the different base numbers separate same thing applies here 8 squared multiplied by 5 squared multiplied by 8 to the 4 x 5 tether that's right 1 and I'm sure you can see what's going on here 5 to the 1 times 5.