 we're getting to be really ugly super fast so what I'm going to do I'm going to leave that one alone because I like the way it looks I'm going to leave this one alone because usually in a really large complicated problem there's always one or two that you know look fairly reasonable that look okay you can deal with right so what we're going to do is we're just going to make take these ones one more level more complicated than even that and again you can take these and just apply so many different things and I'm just basically using multiplication division addition subtraction here there's a lot more other things you can do 125 to a power of a half let's make this more complicated now we'll talk about it one over two you can write as three over six if you want and what I'm going to do is I'm going to keep this down now 125 is five times five times five which is just five two right now I want to kick this down to a denominator so I'm going to apply a negative sign to the exponent so this is going to be one over five two okay let's put this in the bracket now because like this was in the numerator I kicked it down to a denominator adding a negative sign here so what I'm going to do I'm going to create a negative sign now to a power of half I'm going to write that as three over six so I'm going to apply the three here but I'm not going to write the six down there I'm going to take it to a power of one over six and I can write that as two over twelve or whatever right you can just you can you can just continue to make it more complicated and the way it works with exponent to an exponent these guys multiply each other so that's just three over one so three multiplied that's one multiplied that's so three over six and that reduces to half the negative sign you just kick this up right so that gives us that guy so that guy just became uh how long fairly probably I shouldn't be using that this guy now this guy I'm going to add apply a positive negative sorry I have to shift subtraction so what I'm going to do I'm going to write this guy as 16 square root 10 right and to go from 16 to 6 you have to subtract 10 right so I'm going to go minus and you got to make sure you can't just go minus 10 you have to have the square root 10 right you can't you can't go 16 apples minus 10 it has to be 10 apples for you to give to give you six six apples back right it can't be 10 of something else uh as long as you're dealing with certain units we'll talk about that later to get it to you now we have to we have to convert we have to write here minus 10 square root 10 right for this thing to get back six square root 10 but I'm not going to write 10 square root 10 I'm going to write 10 inside and when it comes inside the clones itself so it becomes 10 times 10 it becomes 100 100 times 10 is 1000 so I'm going to write down square root of 1000 so six square root 10 can be written as 16 square root 10 minus square root of 1000 and again this by itself could be one single problem right it would be like you know question number two or something on an exam that you have where you're dealing with the simplifying graph but let's bring the number two inside so that becomes two times two so if you break that inside it becomes two times two and you've got another two there it becomes eight square root eight so I'm going to go square root I'm eight right now I'm going to square root of eight that's the same thing as two square root two I'm going to make this two right that means I added one square root eight here so what I need to do is subtract one square root eight to get back the square root eight which converts into two square root two so find this square root of eight but I'm not going to write down square root eight because I'm saying it's two square root two now you can forget about this guy that was just hard work to get this right so again this guy by itself would be one single question right and they give you a lot of these things because they say combine like terms but straight up you could combine these guys because that's the square root of eight and that's the square root of two so we just made that guy a lot more complicated this guy we're going to leave alone so this guy is going to be minus eight to the power of eight over three and we're going to definitely that guy well we couldn't make that guy more complicated should we make it more complicated let's take it one more level let's convert this into a just subtract or add something so that's what that becomes minus four cube root of eight to the power of five looks like we don't want it to be four it's already a four we want it to be uh let's go I'm going to rewrite four easily as nine so I have to subtract five from nine to get back four so I'm going to find that's five cube root of eight to the power of all divided by two eight to the power of negative two cube root of actually let's do something with that the three here you could write down as write it as a fraction so six divided by two this guy would become eight to the power of six over two just so it doesn't it's not so obvious that that's just eight right because if you take this it becomes the denominator three over three three over three is just one so that would just be eight right so that becomes our final problem and this thing here would be a super hard problem fairly hard problem for high school math I think everybody should be able to do this in my as far as I'm concerned everybody should be able to do this towards the end of grade nine because grade nine grade 10 is where you start dealing with radicals and exponents the rules they just you know they don't give you enough hard problems for you for most most students to figure out that you know there is there's no magic here you're taking the same rules and just you know expanding and reducing and crunching it so consider this what we'll probably end up doing is redoing this problem on another board I don't know where I'm going to do this because it's going to take a lot of space and I only got a tripod so it's a very fixed frame I have here right so I might end up just doing this on a piece of paper but again this is the problem I might even just leave this alone because we've gone through figuring it out you should be able to find your way from us creating this large problem to this level and from here back again I'm not sure how it works if you play the video backwards but maybe it will okay that'll be solving this problem okay hope this helps if it's more complicated later on when I take care of a few other sections I might come back to this and do more problems I know this is really important because this stuff appears all the way through high school and later on because it's it's part of the base level of mathematics the language because you have to deal with radicals and stuff okay hopefully this help it didn't hopefully didn't make you guys more conflict confused with the stuff because you know it looks ugly it really does look ugly okay we'll talk later