### Video instructions and help with filling out and completing Who Form 5495 Index Instructions and Help about Who Form 5495 Index

In this video I'm going to show you how to do with fractional powers so as an example I mean something like 16 to the power of 1/2 the power on that number is a fraction there are certain things you just need to learn the power of 1/2 is the same as a square root so 16 to the power of 1/2 is the same as the square root of 16 square root of 16 is 4 if you're doing higher level you need to remember it's not just for it could also be minus 4 because minus 4 times minus 4 will also give you 16 because minus times a minus makes a plus so it's 4 or it's minus 4 me write that down using this plus or minus symbol here that means plus 4 and minus 4 so if you had 25 to the power of 1/2 that's the same as square root of 25 which is 5 but it could be plus 5 or minus 5 so the power of 1/2 means a square root if you had the power of 1/3 power third means the same as cube root so the cube root we usually write down with the root symbol but was it as a 3 outside it and if we're trying to find the cube root of 8 that means we're trying to find some number that when we write it down 3 times and times that number together we get 8 now if we have 2 times 2 times 2 2 written down 3 times 2 times 2 is 4 times by 2 is 8 so the cube root of 8 is 2 8 to the power of 1/3 is 2 if we look at another one if we look at 27 to the power of 1/3 again that power of 1/3 means you cube root which you write like that means what number do we write down three times and times together to get 27 that was actually 3 because 3 times 3 times 3 is 27 3 times 3 is 9 9 times 3 is 27 you diggin on calculator paper and you're asked to do cube roots they're going to be fairly straightforward you've seen the cube root of 8 is 2 because 2 cubed is 8 3 cubed is 27 4 cubed is 64 5 cubed is 125 if you can remember those that could be very useful so far all the fractional powers we've seen they've got a 1 on the top that's not always the case we could come across something like 125 to the power of 2/3 if you have a fractional indices index a fractional power where the top number isn't a 1 first of all change it so it is a 1 because that's easy to deal with we know that that means the cube root of 125 but you've got to use that to somewhere put that in brackets with the top number of the fraction here if you think back to the laws of indices where you have a power to a power you times those together so 1/3 times by 2 is 2/3 so those are the same thing now 125 to the power of 1/3 it's a cube root of 125 so that's what's inside the bracket that still has to be squared the cube root of 125 is 5 because 5 times 5 times 5 is 125 5 times 5 is 25 times that by 5 you go 125 so that's what's inside the bracket and that has to be squared 5 squared is 25 so 125 to the 2/3 is 25 and the trick there was to make sure you put a 1 there to start with and then the top number the fraction goes outside the bracket so have a look at another one I have a look at 81 to the power of 3/4 so the trick to use here is to rewrite it so it's 81 to the power of 1/4 and then that top number put outside a bracket as an extra power because the rules of indices say a power to a power you times those together in a quarter to the power of three is three quarters so those are the same thing now going through this video we haven't yet come across what a pair of a quarter means but you're probably not going to be very surprised it means the fourth root of 81 and then that has to be cute doesn't forget about that three the fourth root of 81 means what number do I write down for x and x together to get 81 the answer is 3 3 times by 3 is 9 times by another 3 is 27 times by another 3 is 81 so this pit here inside the bracket is 3 and then I have to put that pair of a 3 there as well and mustn't forget that 3 to the power 3 means 3 times 3 times 3 that's 27 so 81 to the power of 3 courses comes out to be 27 have a look at two more examples at this at the moment one to the power of 4/3 1 to the power of anything is always 1 1 to the power 2 means 1 times 1 which is 1 1 to the power of 3 means 1 times 1 times 1 it's still 1 1 to the power of anything is always 1 just worth remembering so it's like a trick question really 1/2 power anything it's just 1 they are all equal to each other if we have a look at another one 9 to the power of minus 1/2 we said in the laws of indices video you haven't watched that one it might be good idea to see that one first how to work with indices that a - power means 1 over