 All right, so a quick one for you today at a year eight level we're going to be operating with indices So with indices we're going to look at addition So with addition you have something like three to the power of two Plus three to the power of four What do we do what do we do so for this one for this one we can evaluate it we can just Get it correct. All right, so with three to the power of two we use bimnas So three to the power of two is also known as three times three which equals to nine Okay, so that's our first number three to the power of four is three times three Times three times three three times three is nine times three is 27 Times three again Equals How do you want how else do we do that? Well, let's break this down. Let's break this down again So when we have three times three My bra buster has just broken When we have three times three a loop all that what do we have? We've got three times three is nine three times three is nine nine times on 81 or 27 27 27 7 14 21 carry the two two four six seven eight 81 and that's how we added them for going too fast repeat that watch it three more times and you will hopefully go Oh, that makes sense Right, let's go back to this so our first number is nine and Our next number is 81 What are they doing together? Plus, what's 81 plus 9? There is your answer Okay, evaluate means solve Find the answer find the solution finish the problem Done, right Now, let's see if we can break this down a little bit more. Okay, how does that become 90? Well three to the power of two So three to the power of two, which means three times three Okay, which means three three three There are three lots of three which equals to nine. Yeah But let's just continue with these. Okay, we've got three lots of Three to the power of four now three to the power of four We've got Three times three times three times three Okay, three lots of three, right? Three lots of three We've done that Okay, we've done that part, but that's saying that there's three lots of three of three So we have to write these three more times. So three three three three three Okay, three lots of three of three Yeah, what about three lots of three lots of three lots of three. So we have to do that Another three more times. So three lots of three And you keep doing it forever, okay, so With this one we've got two Three and four. We've got this at nine. We've got this at 27 now for this one we had this correct now for the first one we had nine So it's adds up to nine. Then we had another nine And then we had another nine Okay, nine nine and nine Equals 27 Okay, and then we had another group And we know that as 27 and then we had another group and we know that as 27 and we added all those groups up, right and then we got 81 and then we added all those threes together with these three and we got 90 Now see how long that took us That took us a long time didn't it writing all these threes down. Okay, imagine even bigger numbers We'd be here all day we run out of ink would run out of whiteboard We'd run out of battery on our iPads would run out of paper in our notebooks just writing threes all day All right, especially if it was to the power of ten. Can you imagine? I don't think we'd have enough time in the day as well So we use indices to simplify it. Okay to make it smaller and then all we had to do was go Three to the power of three three times three Three to the power of four times three times three times three twenty seven eighty one and then add them together Okay Now when these numbers get bigger the calculators become more handy. Let's move on the next one is multiplication now multiplication There's even more hardcore Or is it so let's do the multiplier section Let's have a problem. Let's go the same numbers. We've got three to the two times three to the four Here's our first Indici law All right, here's our first indice a lot We're gonna call this the base number so label this that's the base Number Whatever number it is. That's the base number this We now know as the indice Little number at the top little cute little number little bird sitting on top of the the number right pecking at it now If both numbers are the same Stays the same But what do we do to the little numbers when we multiply? Here's the indice law one And I'm going to use algebraic terms right so any base number Multiply by that same base number if it has M amount and n amount What actually happens is? They both come together because they're the same and the m and the n actually add So let's say we've got these values here that stays the same what two numbers add up That's right the two and the four Which equals? Three to the power of six Let's prove that theory. Let's prove that theory So we have three to the power of two We know that it's three times three. How many threes can you see? To that's why it's a two Three to the power of four Yeah, just like our last problem. How many threes can you see and what are they all doing together? Multiply how many threes are there all together? six That's why it's a six now Same rules apply same same rules apply. Okay. I'm going to give you a different answer I'm going to jumble these around I'm going to go divide Here's the next indice law Three to the power of six three to the power of four and we have a base number. That's the same the n and the n Subtract so when we divide our indices with the same base value the indices subtract Six take four. Oh, we skipped the step. Didn't we? What's our base number here? three Six take four is Done, that's our answer sweet. Cool. Yeah Shall we do the theory as well? Let's do the theory. How many threes are there three times three times three Times three times three times three There are six threes there. We'll find all together over here. We've got three times three times three times three times three And take that one. There we go four of them. Yeah, because we're dividing and our rule is and take away and Well, we don't even have to write that we just have to take away four from here And we're left with three times three and three times three an industry form is three to the power of two done All right, that is that one all sorted. So that's our main Indice laws Then you get the tough one you get this really annoying one you get three to the power of three to the power of four Brackets. Oh boy. Oh boy So, what does that mean the industry law here is this X? Bracket three Sorry, I'm going to use the letters again to make more sense because we can't put values in and and What are these two doing together? Have a think pause it and have a think write down what you think the answer is and What they're actually doing is multiplying so m times Okay, they're not adding their times. So let's let's show you why I'll show you why on this board So let's go inside the brackets three times three to the power of three We know that that as three times three times three To the power of four is saying it four times. So we have to write this in total four times Let's do it. Let's do it. Just to show you Three one more So four lots of them. So there's one row two three four lots of The original amount of three times three, okay Now if we follow this law of m times n We're multiplying three times four three times four equals 12 and We keep the same base number. So it'll be three to the power of 12 They're all multiplying together How many threes do you reckon I wrote down here? 12 let's count three six nine 12 We're done. We've done it there. We've done it You're welcome There are more in to see those and we'll cover them eventually very shortly after these short messages Hope you enjoyed it