Learn about Exponent Rules Part 2 Video

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Learn about Exponent Rules Part 2

Welcome to part 2 on the presentation on level one exponent rules. So let’s start off by reviewing the rules we’ve learned already. If I had 2^10 x 2^5 we learned that, since we’re multiplying exponents with the same base, we can add the exponents so this equals to the 15th. We also learned that if it was 2^10 over 2^5 we would actually subtract the exponents. So this would be 2^10 - 5 which equals 2^5, and the end of the last presentation and I probably should not introduced it so fast. I enter this to new concept. What happens if I have (2^10)^5. Well let’s think about what that means. When I raise something to the 5th power that’s just like saying 2^10 x 2^10 x 2^10 x 2^10 x 2^10, all I did I took 2^10 and I multiply it by itself 5 times. So that’s what 5th power. Well we know from this rule up here that we can add these exponents because they’re all the same base. So if we add 10+10+10+10+10 what do we get? We get 2^5th power. So essentially what did we do here? All we did is we multiplied 10x5 to get 50 so that’s our 3rd exponent rule. Is that when I raise an exponent to a power and then I raise that whole expression to another power, I can multiply those two exponents. So let me give you another example, if I said 3^7 and all of that to the (-9).Once again, all I do is I multiply the 7 and the (-9) and I get 3(^-63). So you see it works that just as easily with negative numbers. So now I’m going to teach you one final exponent property. If I have, let’s say I have 2 times say 9 and I raise that whole thing to the 100 power, it turns out that this is equal to 2^100x9^100 and let’s make sure that that make sense so let’s do it with the smaller example. What if it was (4x5)^3? Well that was just be equal to (4x5)(4x5)(4x5) which is the same thing as 4x4x4x5x5x5, I just switch the order which I’m multiply what you can do with multiplication. And then 4x4x4, well that’s just equal to 4^3 and 5x5x5 is equal to 5^3. Hope that gives you a good intuition of why this property here is true and actually when I have first learned exponent rules, I would always forget the rules and I would always do this proof myself or the other proofs and the proof is just an explanation of why they all works just to make sure that I was doing it right. So given every thing that we’ve learned now, actually let me review all of the rules again. If I have 2^7x2^3, well then I can add the exponents to 10th. If I have 2^7 over 2^3, well here I subtract the exponents and I get 2^4. If I have (2^7)^3 well here I multiply the exponent that gives you 2^21 and if I had (2x7)^3, well that equals to the 3rd times 7^3. Now let’s use all of these rules we’ve learned to actually try to do some what I will call them composite problems that involved you using multiple rules at the same time and a good composite problem was that problem that I had introduced you to at the end of that last seminar. So if I said, let’s say I have 3²x9^8 and all of that I’m going to raise to the (-2) power. So what can I do here? Well 3 and 9 are two separate basis but 9 can actually be expressed as an exponent of 3 right, 9 is the same thing as 3². So let’s rewrite 9 like that. Say that’s equivalent to 3² times 9 is the same thing as (3²)^8 and then all of that to the (-2) power. All of these are placed 9 with 3² because we know 3x3 is 9. Well now we can use the multiplication rule on this to simplify it. So this is equal to 3² (3^2x8) which is 16 and all of that (^-2). Now we can use the first rule, we have the same base so we can add the exponents and were multiplying them. So that equals 3^18 right, 2 + 16 and all of that to (-2). And now were almost done. We can once again use this multiplication rule and we can say 3, this is equal to 3^18x(-2). So that’s 3^(-36). S o this problem minus seemed pretty daunting at first but there aren’t that many rules. And all you have to do is keep seeing oh wow that little part of the problem I can simplify it and then you simplify it and you’ll see that you can keep using rules until you get to a much simpler answer. And actually the level one problems don’t even involve problems this difficult. This will be more on the exponent rules level 2. But I think at this point you’re ready to try the problems. I’m kind of divided whether I want you to memorize the rules because I think its better to almost forget the rules and have to prove it to yourself over and over again to the point that you remember the rules because if you just memorized the rules later on in life when you haven’t done it for a couple of years, you might kind of forget the rules and then you won’t know how to get back to the rules. But it’s up to you. I just hope you do understand why this rules work and as long as you practice and you pay attention to the signs, you just don’t have no problems with the level one exercises, have fun.

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Welcome to part 2 on the presentation on level one exponent rules. So let’s start off by reviewing the rules we’ve learned already. If I had 2^10 x 2^5 we learned that, since we’re multiplying exponents with the same base, we can add the exponents so this equals to the 15th. We also learned that if it was 2^10 over 2^5 we would actually subtract the exponents. So this would be 2^10 - 5 which equals 2^5, and the end of the last presentation and I probably should not introduced it so fast. I enter this to new concept. What happens if I have (2^10)^5. Well let’s think about what that means. When I raise something to the 5th power that’s just like saying 2^10 x 2^10 x 2^10 x 2^10 x 2^10, all I did I took 2^10 and I multiply it by itself 5 times. So that’s what 5th power.

Well we know from this rule up here that we can add these exponents because they’re all the same base. So if we add 10+10+10+10+10 what do we get? We get 2^5th power. So essentially what did we do here? All we did is we multiplied 10x5 to get 50 so that’s our 3rd exponent rule. Is that when I raise an exponent to a power and then I raise that whole expression to another power, I can multiply those two exponents. So let me give you another example, if I said 3^7 and all of that to the (-9).Once again, all I do is I multiply the 7 and the (-9) and I get 3(^-63). So you see it works that just as easily with negative numbers.

So now I’m going to teach you one final exponent property. If I have, let’s say I have 2 times say 9 and I raise that whole thing to the 100 power, it turns out that this is equal to 2^100x9^100 and let’s make sure that that make sense so let’s do it with the smaller example. What if it was (4x5)^3? Well that was just be equal to (4x5)(4x5)(4x5) which is the same thing as 4x4x4x5x5x5, I just switch the order which I’m multiply what you can do with multiplication. And then 4x4x4, well that’s just equal to 4^3 and 5x5x5 is equal to 5^3.

Hope that gives you a good intuition of why this property here is true and actually when I have first learned exponent rules, I would always forget the rules and I would always do this proof myself or the other proofs and the proof is just an explanation of why they all works just to make sure that I was doing it right. So given every thing that we’ve learned now, actually let me review all of the rules again. If I have 2^7x2^3, well then I can add the exponents to 10th. If I have 2^7 over 2^3, well here I subtract the exponents and I get 2^4. If I have (2^7)^3 well here I multiply the exponent that gives you 2^21 and if I had (2x7)^3, well that equals to the 3rd times 7^3. Now let’s use all of these rules we’ve learned to actually try to do some what I will call them composite problems that involved you using multiple rules at the same time and a good composite problem was that problem that I had introduced you to at the end of that last seminar. So if I said, let’s say I have 3²x9^8 and all of that I’m going to raise to the (-2) power. So what can I do here?

Well 3 and 9 are two separate basis but 9 can actually be expressed as an exponent of 3 right, 9 is the same thing as 3². So let’s rewrite 9 like that. Say that’s equivalent to 3² times 9 is the same thing as (3²)^8 and then all of that to the (-2) power. All of these are placed 9 with 3² because we know 3x3 is 9. Well now we can use the multiplication rule on this to simplify it. So this is equal to 3² (3^2x8) which is 16 and all of that (^-2). Now we can use the first rule, we have the same base so we can add the exponents and were multiplying them. So that equals 3^18 right, 2 + 16 and all of that to (-2).

And now were almost done. We can once again use this multiplication rule and we can say 3, this is equal to 3^18x(-2). So that’s 3^(-36). S o this problem minus seemed pretty daunting at first but there aren’t that many rules. And all you have to do is keep seeing oh wow that little part of the problem I can simplify it and then you simplify it and you’ll see that you can keep using rules until you get to a much simpler answer. And actually the level one problems don’t even involve problems this difficult. This will be more on the exponent rules level 2. But I think at this point you’re ready to try the problems. I’m kind of divided whether I want you to memorize the rules because I think its better to almost forget the rules and have to prove it to yourself over and over again to the point that you remember the rules because if you just memorized the rules later on in life when you haven’t done it for a couple of years, you might kind of forget the rules and then you won’t know how to get back to the rules. But it’s up to you. I just hope you do understand why this rules work and as long as you practice and you pay attention to the signs, you just don’t have no problems with the level one exercises, have fun.

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