Hi everyone thanks for watching my online lesson on fractional and negative indices, so some of the most simple questions like the first and second one here do actually appear on foundation tier, but i said that this video is higher only because i am going to go through some more complicated examples which are only higher tier, so the few different things we need to know so the first one is what happens when my indices are negative.

So this first one here i’ve got 3 to the power of minus 2, so we should know that 3 to the power of 2 or 3 squared is just 9 and what the negative does is. It makes my answer the reciprocal of that, so it’s 1 over 9.

The next thing is what happens where my index number is a fraction, so here i have 36 to the power of 1/2. Now looking at whatever number is on the bottom of the fraction. So here the number on the bottom of the fraction is just a 2! It means i’m finding the square root! If this was a 3 i’d be finding the cube root? If it was a far i’ll be finding the fourth root and so on so here i just want what is the square root of 36, and that is 6? This next one’s weight gets slightly more complicated because i have a number. That’s not 1 on the numerator of my fraction and i have a 3 on the denominator? So, as i said before, the 3 on the denominator means i’m?

Gonna find the cube root of 27 i’m, going to deal with that first, so i’m gonna do what is the cube root of 27 and the cube root of 27 is just 3! Now, that’s not the answer.

That’s the answer to 27 to the power of 1/3 i have 27 to the power of 2/3 and that 2 on the top on the numerator means i’m just going to square this, so i’m actually doing is finding 3 squared, which is 9? That’s my answer, and this last one is a very complicated example, because not only do i have a fraction, it’s 3/4 i?

Also it’s a negative as well, and the thing i’ve got in brackets is a fraction, so it’s really complicated? So i’m going to deal this step by step, so the first thing i’m going to do is i’m going to deal with this four at the bottom of the fraction. That means it’s a faster route, so this here means i’m finding the fourth root. So what number times by itself and again and again, gives me and i’m going to treat the fraction separately so the fourth root of 16 is 2 and the fourth root of 81 is 3! That’s 2/3, so i’ve dealt with that far on the bottom.

I still need to deal with the minus 3. So now i’m going to cube everything so 2 cubed is 8 and 3 cubed is 27. So that’s the 3 dealt with, but i still need to deal with the minus 1 and, as i said before, when it’s a minus index number, it means i’m finding the reciprocal so i have to flip this fraction over and that’s 27 over 8. That is the most complicated example.

I have managed to find on fractional and negative indices. Here’s a few questions for you to try test in a few of the different skills. I’ve also put 7 to the power of 0 in there to check you know what to do. There i’ve not included a question where you dealing with a fraction purely because i couldn’t find another question that was as complicated as the last example. I just did but pause. The video have a go at these questions and then unpause when you’re ready to see the solutions. Here are the answers, so 36 ^ 1/2 is just square roots in it. So that’s 6, 3, ^, -, 2 or 3 ^ 2 is 9, so that’s 1 over 9, 7, ^ 0.

Well, anything ^ 0 is just 1 and 4 ^ -1. It just means do the reciprocal of 4, so it’s 1 over 4 and then the next to that a slightly more complicated i’ve done a few steps of working out – the first one, 64 ^ 1/3 would mean cube root it so that’s far but 65 to the power of 2/3 after then square. My far so that’s 16 and the second one i’m going to deal with some steps as well. So the first thing is 8 ^ 1/3 would be too because that’s cube root in it, but the 2 on the top i have to square my 2, so i get 4 and then because it’s a negative index number i have to do the reciprocal of 4! So that’s 1 over 4! Thank you for watching. .