Learn about Exponent Rules Part 1 Video

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Learn about Exponent Rules Part 1

Welcome to the presentation on level one exponent rules. Let’s get started with some problems. So if I were to ask you what two, that’s a little fatter than I want it to be but let’s just keep it fat so that looks clear, 2^3 times, and dot is another way of saying times. If we’re to ask you to a 2^3x2^5 is, how would you figure that out? So 2^3x2^5, well there’s one way that I think you do know how to do it. You could figure out that 2^5 is 8 and that 2^5 is 32 and then you could multiply them, and what? 8x32 is this 240 plus it’s 256. You could do it that way and that’s reasonable because it’s not that hard to figure out what 2^3 is and what 2^5 is. But if those were much larger numbers this method might become a little difficult. So I’m going to show you using exponent’s rules you can actually multiply exponentials or exponent numbers without actually having to do as much arithmetic or actually you can handle number much larger than your normal math skills might allow you to. So let’s just think about what 2^3x2^5 means. 2^3 is 2x2x2 and were multiplying that times 2^5 and that’s 2x2x2x2x2. So what do we have here? We have (2x2x2)(2x2x2x2x2) really all we’re doing is we’re multiplying 2 how many times? Well 1 2 3 4 5 6 7 8. So that’s the same thing as 2^8, interesting. 3+5 is equal to 8 and that make sense because 2^3 is 2 multiplying by itself 3 times, to the 5th is 2 multiplying by itself 5 times, and then we’re multiplying the twos, we’re going to multiply it to 8 times. I hope I achieved my goal of confusing you just now. Let’s do another one. If I said 7² x 7^4, that’s a four. Well that equals 7x7, write that 7^2 times, and now let’s do 7^4; 7x7x7x7. Well now we’re multiplying 7 by itself 6 times so that equals 7^6. So in general whenever I’m multiplying exponents of the same base that’s the key, I can just add the exponents so 7^100x7^50 and notice this is an example now, it’d be very hard without a computer to figure out what 7^100 is and likewise very hard without a computer to figure out what 7^50 but we could say that this is equal to 7^100+50 which is equal to 7^150. Now I just want to give you a little bit warning, make sure that you’re multiplying because if I had 7^100+7^50, there’s actually very little I could do here. I couldn’t simplify this number. So I’ll throw out one to you just, if I had 2^8x2^20, well we know we can add this exponents. So that gives you 2^28 right? What if I had 2^8+2^8? This is a bit of a trick question. Well I just said if we’re adding we can't really do anything. We can't really simplify it but there’s a little trick here is that we actually have two 2^8 right. There’s 2^8x1, 2^8x2 so this is the same thing as 2(2^8), doesn’t it? 2(2^8) that’s just to 2^8 plus itself and 2(2^8) well that’s the same thing as 2^1x2^8 and 2^1x2^8 by the same rule we just did is equal to 2^9. So I thought I would just throw that out to you and it works even with negative exponents. If I were to say 5^(-100) times 5^102, that would equal 5², I just take (-100)+102, this is a 5 and that of course that equals to 25. So that’s the first exponent rule. Now I’m going to show you another one and it kind of leads from the same thing. If I were to ask you what 2^9 over 2^10 equals, that looks like that could be a little confusing. But it actually turns out to be the same rule because what’s another way of writing this? Well we know that this is also the same thing as 2^9x½^10 right? And we know 1/2^10 well, you could rewrite this as 2^9 x 2^(-10) right. All I did is I took ½^10 and I flip it and I made the exponent negative and I think you know that all ready from level 2 exponents. And now once again we can just add the exponents 9 + (-10) equals 2^(-1) or we could say that equals ½ right. So that’s an interesting thing here. Whatever is the bottom exponent you could put it in the numerator like we did here but turn into a negative so that lead us to the second exponent rule. A simplification is we could just say it that this equals 2^9-10 which equals 2^(-1). Let’s do another problem like that. If I said, 10^200 over 10^50 well that’s just equals 10^200-50 which is 150, likewise if I had 7^48 over 7^(-5) this will equal 7^40-(-5) so it equals 7^45. And now what you think about that is that makes sense? Well we could have re-written this equation as 7^48x7^5 right? We could have taken this 1/7^(-5) and turn it into 7^5 and that would also just be 7^45. So the second exponent rule I just taught you actually is no different than that first one. If the exponent is in the denominator and of course it has to be the same base and you’re dividing, you subtract it from the exponent and the numerator. If they’re both on the numerator, as in this case 7^48x7^5 actually there’s no numerator but if they’re essentially multiplying by each other and of course you have to have the same base, then you add the exponents. Now I’m going to add one variation to this and actually this is the same thing but it’s a little bit of a trick question. What is 2^9x4^100? Actually, maybe I shouldn’t teach this one so you have to wait until I teach you the nest rules but I’ll give you a little hint. This is the same thing as 2^9(2²)^100 and the rule I’m going to teach you now is that when you have something to an exponent and then that number raise to an exponent, you actually multiply these two exponents. So this would be 2^9x2^200 and by that first rule we learned this would be 2^209. Now in the next module, I’m going to cover this in more detail. I think I might have just confused you but watch the next video and then after the next video I think you’re going to be ready to do level 1 exponent rules. Have fun.

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Welcome to the presentation on level one exponent rules. Let’s get started with some problems.

So if I were to ask you what two, that’s a little fatter than I want it to be but let’s just keep it fat so that looks clear, 2^3 times, and dot is another way of saying times. If we’re to ask you to a 2^3x2^5 is, how would you figure that out? So 2^3x2^5, well there’s one way that I think you do know how to do it. You could figure out that 2^5 is 8 and that 2^5 is 32 and then you could multiply them, and what? 8x32 is this 240 plus it’s 256. You could do it that way and that’s reasonable because it’s not that hard to figure out what 2^3 is and what 2^5 is. But if those were much larger numbers this method might become a little difficult. So I’m going to show you using exponent’s rules you can actually multiply exponentials or exponent numbers without actually having to do as much arithmetic or actually you can handle number much larger than your normal math skills might allow you to.

So let’s just think about what 2^3x2^5 means. 2^3 is 2x2x2 and were multiplying that times 2^5 and that’s 2x2x2x2x2. So what do we have here? We have (2x2x2)(2x2x2x2x2) really all we’re doing is we’re multiplying 2 how many times? Well 1 2 3 4 5 6 7 8. So that’s the same thing as 2^8, interesting. 3+5 is equal to 8 and that make sense because 2^3 is 2 multiplying by itself 3 times, to the 5th is 2 multiplying by itself 5 times, and then we’re multiplying the twos, we’re going to multiply it to 8 times. I hope I achieved my goal of confusing you just now. Let’s do another one. If I said 7² x 7^4, that’s a four. Well that equals 7x7, write that 7^2 times, and now let’s do 7^4; 7x7x7x7. Well now we’re multiplying 7 by itself 6 times so that equals 7^6.

So in general whenever I’m multiplying exponents of the same base that’s the key, I can just add the exponents so 7^100x7^50 and notice this is an example now, it’d be very hard without a computer to figure out what 7^100 is and likewise very hard without a computer to figure out what 7^50 but we could say that this is equal to 7^100+50 which is equal to 7^150. Now I just want to give you a little bit warning, make sure that you’re multiplying because if I had 7^100+7^50, there’s actually very little I could do here. I couldn’t simplify this number. So I’ll throw out one to you just, if I had 2^8x2^20, well we know we can add this exponents. So that gives you 2^28 right? What if I had 2^8+2^8? This is a bit of a trick question.

Well I just said if we’re adding we can't really do anything. We can't really simplify it but there’s a little trick here is that we actually have two 2^8 right. There’s 2^8x1, 2^8x2 so this is the same thing as 2(2^8), doesn’t it? 2(2^8) that’s just to 2^8 plus itself and 2(2^8) well that’s the same thing as 2^1x2^8 and 2^1x2^8 by the same rule we just did is equal to 2^9. So I thought I would just throw that out to you and it works even with negative exponents. If I were to say 5^(-100) times 5^102, that would equal 5², I just take (-100)+102, this is a 5 and that of course that equals to 25.

So that’s the first exponent rule. Now I’m going to show you another one and it kind of leads from the same thing. If I were to ask you what 2^9 over 2^10 equals, that looks like that could be a little confusing. But it actually turns out to be the same rule because what’s another way of writing this? Well we know that this is also the same thing as 2^9x½^10 right? And we know 1/2^10 well, you could rewrite this as 2^9 x 2^(-10) right. All I did is I took ½^10 and I flip it and I made the exponent negative and I think you know that all ready from level 2 exponents. And now once again we can just add the exponents 9 + (-10) equals 2^(-1) or we could say that equals ½ right. So that’s an interesting thing here. Whatever is the bottom exponent you could put it in the numerator like we did here but turn into a negative so that lead us to the second exponent rule. A simplification is we could just say it that this equals 2^9-10 which equals 2^(-1). Let’s do another problem like that.

If I said, 10^200 over 10^50 well that’s just equals 10^200-50 which is 150, likewise if I had 7^48 over 7^(-5) this will equal 7^40-(-5) so it equals 7^45. And now what you think about that is that makes sense? Well we could have re-written this equation as 7^48x7^5 right? We could have taken this 1/7^(-5) and turn it into 7^5 and that would also just be 7^45. So the second exponent rule I just taught you actually is no different than that first one. If the exponent is in the denominator and of course it has to be the same base and you’re dividing, you subtract it from the exponent and the numerator. If they’re both on the numerator, as in this case 7^48x7^5 actually there’s no numerator but if they’re essentially multiplying by each other and of course you have to have the same base, then you add the exponents.

Now I’m going to add one variation to this and actually this is the same thing but it’s a little bit of a trick question. What is 2^9x4^100? Actually, maybe I shouldn’t teach this one so you have to wait until I teach you the nest rules but I’ll give you a little hint. This is the same thing as 2^9(2²)^100 and the rule I’m going to teach you now is that when you have something to an exponent and then that number raise to an exponent, you actually multiply these two exponents. So this would be 2^9x2^200 and by that first rule we learned this would be 2^209.

Now in the next module, I’m going to cover this in more detail. I think I might have just confused you but watch the next video and then after the next video I think you’re going to be ready to do level 1 exponent rules. Have fun.

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