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Current time:0:00Total duration:3:32

Video transcript

we have three times X to the power of a times B X to the fourth power and we have that equaling negative 24 X to the sixth and so what I'd like you to do is pause this video and see if you can figure out what a and B need to be well to figure this out we can just multiply out this left-hand side so let's do that so what we have right over here we can just rewrite that is 3 times X to the power of a times B times X to the fourth and we could rewrite this as we can just change the order which is multiplying four different things this is the same thing as three times B times X to the a times X to the fourth and if you were doing this on your own you wouldn't have to do all of these steps but hopefully this makes it clear what's actually going on and what's this going to be well we have our let me do this in a new color we have our 3b here so that is three B and what's X to the a times X to the fourth X to the a times X to the fourth I have the same base raised to different exponents and I'm multiplying the two well we know from our from our exponent properties this is going to be the same thing as X to the a plus four X to the a times X to the fourth is X to the a plus four we're just adding the exponents because we have the same base and we're multiplying these two so we now have that 3b is equal to X to the a plus fourth power and this is going to be equal to what we have on the right hand side so this is going to be equal to in that same color negative 24x to the sixth so what can we do now well we can recognize that 3b is going to have to be equal to negative 24 and the a plus 4 right over here is going to need to be equal to the 6 so let's write that down 3b is equal to negative 24 3b is equal to negative 24 you might be able to do that in your head or if you want to do a little bit more systematically divide both sides by three to solve for your B and you get B is equal to negative eight and we can also say that a plus four is equal to 6 subtract 4 from both sides you get a is equal to 2 and we are done and you can check it if you want we can rewrite it as if we say a is equal to 2 we could say 3x squared times instead of B we know that's negative 8 negative 8 X to the fourth what is that going to be equal to 3 times negative 8 is negative 24 x squared times X to the fourth is X to the sixth and once again as I said you don't you wouldn't necessarily have to do all of these steps on your own if you're doing it on paper but this is what you're doing if you look at this look at the original problem you say okay the coefficients I can multiply those three times B to get this coefficient over here so 3 times B is negative 24 B would have to be negative 8 so B would have to be negative 8 here and you can say X to the a times X to the fourth is X to the sixth so well let's see we're going to add exponents 8 plus 4 is going to be equal to 6 a must be equal to 2 so you might be able to do it that's simply but this is what you're doing if you even if you're doing it in your head like that