Transcript for:
Understanding and Applying Exponent Rules

in the previous lessons we've been learning about all of the different exponent rules let's quickly summarize what they were and then what we're going to do is we're going to use all four of them together in this lesson so we're going to have uh questions like that that and a whole bunch of others coming up okay so um exponent rule one exponent rule two and then we did three and four okay so with the first one we had something like 2 3 * by 2 5 and what we learned was when the bases are the same what do we do with the exponents we add because we multiplying over here we add the exponents and so that became 2 to the^ of 8 that was the first type we looked at with exponent rule number two we had something like 3 to the 8 ided 3 to the 2 and what we learned when the bases are the same and you're dividing then what do you do with the exponents well first of all you leave the base you don't change the base and then what do you do with the exponents you minus them and so 8 - 2 I was going to say 8 - 2 over here but 8 - 2 is 6 okay and then we learned if you have something like 3 to ^ of 2 and then there's a number on the outside here then what you do is you leave the base you see how we always leave the base okay and then what we learned was that we multiply those numbers together and then the last one we learned is a very easy one if you have anything to the power of Z then the answer becomes a one so anything to the power of Z so any to the power of0 equal 1 okay so those are the different things you need to understand if you don't understand them then you need to go watch some of those lessons make sure you understand all of the exponent rules because now we are going to go and practice all of them combined and so now we're going to do a whole bunch of examples but I've left these four little rules um now remember these are just example rules okay so what I'm trying to show you is that when when you have a situation like this where you're multiplying you leave the bases the same and then you add because 3 + 5 is 8 when you get something like this you leave the base the same and then you subtract okay and then um here you leave the base the same and then you multiply and then anything to the power of Z is 1 those are the four rules you need to know so let's begin here we're going to just go from left to right so here we have a situation that looks like a divide so what do we know we know that you keep the two two the same so it stays at two right and then what do we do with these exponents you subtract them so what does 8 take away 3 that'll be five Okay so we've done these two and now we're just going to say that over there okay now it looks like we have a situation where we have a rule number one so what do we do we know that we keep the bases the same you see how the two and the two stays a two you mustn't say 2 * 2 is 4 and then what do you do with these ones will you add them how easy is this guys if you just follow your rules it's pretty straightforward so the final answer will be two to the power of 9 let's do a couple more okay so this looks really intimidating right but now you could think of this in different ways you could say okay should we start using rule number three because we've got a bracket or what could we do well there's different you could do it like that if you want to not a problem but what I'm going to do is I'm going to start inside the bracket so I'm going to say okay we have a rule number one over there so we know that we are going to keep it as a three and then we going to add the exponents okay and then we have that but I keep the bracket because I didn't do anything with the bracket yet now I'm going to keep looking inside here and I'm going to say okay this looks like a rule number two and so what rule number two tells us is that you keep the base the same and then what do you do with these numbers you minus them so what is 6 - 5 that is a one and now we have this now all of a sudden we are at a situation that looks like rule number three and so what rule number three tells us to do is you keep the base the same can you see that you keep the base the same and then what do you do do with these two numbers you multiply them right so what are we going to do with those two numbers we're going to multiply them and there is your answer now what if you wanted to rather do this in a different way okay so method for those of you that are happy with this you can go ahead to the next one but for those of you that maybe wanted to try it in a different way well what you could do is 3 4 * 3 2 / 3 5 so maybe because you looked at this and you said that looks like this that's absolutely fine so what we do is we're going to take this one and what do we do with these numbers you multiply them so that's going to become 3 to the^ of 12 then you're just going to do it with this one as well so what does um that become well that becomes 3 The Power of Six because remember we are multiplying and then you can say divide w that's a horrible divide and then you're going to say 3 * 5 which is uh 15 there we go now going into the next step you could say oh that's rule number one so what do we do we keep the threes the same and then what do we do with these exponents we add them so what do we do with these exponents we add them and that's 18 now this is rule number two because we're dividing so what do we do we keep it as a three and then what do we do with these numbers well what did we do over here you subtract so we're going to say 18 - 15 which is three hello hello same answer right so with this one I would start right here in the beginning and I can immediately say oh that is definitely a rule number three and in fact it looks almost exactly the same so what we do is we keep it as a three and then what are we supposed to do with these two numbers well we multiply so what is 2 multip for 8 then I write all the rest down as the same okay now that is rule number one so what do we do we keep it as a three and what do we do with these two numbers well what did we do over here we add them okay so 8 + 2 is 10 now we have a rule number two so with rule number two when you're dividing we keep these numbers the same so that will be a three and then what do we do with these numbers well over here we subtract so that means we're going to say 10 minus 5 which is 5 okay here is our next one so immediately I look at this and I see that it's to the power of Z and from rule number four we know that anything to the power of 0 is one so anything anything to the power of Z is a one okay that takes a lot of well that simplifies things nicely for us now you can just ignore this one because if you say 1 * 4 it's 4 if you say 1 * 10 it's 10 so by putting a one there can you see that it doesn't change the number okay so we don't need to have this one over here so we can actually just rewrite this entire thing as that because 1 multiplied by 3 to 5 is 3 to 5 okay now here is rule number two so oh and it's actually exactly written as we had the examples of here so remember these are just examples he so we know then that that if you have a 3 to 5 and a 3 to the 2 it stays a three and then what do you do with these exponents you subtract them and so that will become 3 to the 3 here's our last example so immediately you could take these two together or you could take all three of of these together if you want to I'm going to take all three together we know that when these are all the same and you're multiplying that is rule number one so with rule number one you keep it as a two and then what do you do with these numbers you add them so what is 6 + 3 + 4 that is 13 okay and then divide and then let's just go write this down okay now if you look at this part that is a rule number three and so what then happens whoops divide is that you keep it as a two and then what do you do here well what did we do over here we multiply so that'll be 2 10 now all of a sudden we have a divide so that is rule number two and so that will become two and then what do we do with these numbers you subtract so what is 13 - 10 3