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### Instructions and Help about Are Form 8815 Index

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 again our fifth video where we discuss dividing indices now before we get going I want to use a skill that we know previously from fractions if someone asked you have asked you to evaluate 12/20 what might you do well let me tell you what I do I'd write that as 12 over 20 like that I'd write the division as over and I'd go away and I try and simplify this fraction by working at the highest common factor in my head of 12 and 20 which I know is 4 and that divide top and bottom by 4 but you remember when I first introduced that idea to you I said write it as for lots of 3 over 4 lots of 5 and really dividing by 4 you can also think of that as canceling the 4 from top and bottom leaving you with 3/5 like that ok so there's a skill I want you to remind yourself on from what we've previously done on fractions and in particular canceling a factor on the top and bottom of a fraction or think of it as dividing the top and bottom in this case by 4 so there's a little skill I want you to think about right let's move on to dividing indices suppose someone said what is 7 to the power of 5 divided by 7 cubed in the same vein as I just showed you would you mind if I wrote that as 7 to the 5 over 7 cubed I hope not and then if we actually wrote out 7 to the 5 as a product and 7 cubed as a product we would have 7 x 7 x 7 x 7 x 7 / or / 7 cubed which we can write as 7 x 7 x 7 now just like when we were simplifying or cancelling our fractions there's a factor ins of 7 on top and bottom which we can divide top and bottom by 7 or cancel the 7 similarly here and similarly here so what are we left with we're left with 1 on the bottom and 7 x 7 on the top which is 7 squared over 1 which we can just write 7 squared now look let me just go right the question 7 5/7 3 got us 7 2 can you see what I'm trying to show you what I'm trying to show you is when the base number is the same and you are dividing indices you can do what with the powers you can do 5 take away 3 is 2 you can subtract the powers to do it in a quicker way and that's what you need to know for dividing indices so let's formalize that dividing indices let's write this down if the base numbers is the same when dividing numbers in index form you can subtract the powers and let's give ourselves an example make up 1 let's say something like 2 to the power of 10 divided by 2 to the power of I don't know 7 would be 2 to the 10 subtract 7 ie which would be 2 to the power of 3 or 2 cute right and just before I move on just one that while I've got the opportunity point out one little similarity from something we've learned previously 5 to the 9 divided by 5 squared would therefore be 5 to the power of 9 take away 2 which is 7 now what about 5 to the 9 multiplied by 5 to the negative 2 when you're multiplying you can add the powers and 9 add negative 2 is also positive 7 and I just want to take the opportunity to point this out it's useful in future learning dividing by 5 squared is the same as multiplying by 5 to the negative 2 let me say again in a different way dividing by 5 squared is the same as multiplying by its reciprocal 5 to the negative 2 and we've seen that before do you remember when I've said things like dividing by a fraction is the same as multiplying by its reciprocal well here dividing by this power is the same as multiplying by its reciprocal so I just wanted to point out the link between multiplication and division again there for you but we're not going to go too much into that in this video it's just for links and building our mathematical strength in our head right let's do some questions on dividing indices simplify the following leaving your answer in index form 9 to the 5/9 to the 3 we can subtract powers that's going to be 9 to the 2 it just said simplify and leave an index form it didn't say evaluate and give me the answer 8 squared divided by 8 to the 4 that's 8 to the to take away 4 by the symmetry of subtraction that's 8 to the negative 2 don't think you've got to do the big number 4 take away 2 first and say that's 8 squared it isn't it's to take away 4 do it in the way you see it ok so be careful not to make this little booboo here it's a common mistake 2 to the power 4 divided by 2 to the put in the power of 1 that's right and subtract the powers and you'd get 2 cubed 3 to the 7 divided by 3 to the 6 is 3 to the seventh a Kawai 6 which we could write as 3 to the 1 ok pause the video and try these ones now you remember over just means divide again so 7 to the 5 divided by 7 to the 2 is 7 to the 5 take away 2 7.

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