Thank you so much. I have been quarantined so I can’t be in school . You saved me from a meltdown because the practice problems that my teacher gave me look nothing like what I learned. You’re a good teacher!
This is a good question, as one of our tactics in simplifying is to combine whatever we can. The reason we don't add exponents here is for 2 reasons... First, we can only do the *add the exponents* trick if we are multiplying together two factors that have the same base. Since 7^(1/3) and 2^1 have different bases, 7 and 2, that option isn't available. Secondly, when faced with division like we see in the fraction, the property would have us *subtract the exponents* to simplify, but again, only if those terms have the same base. It's great that you're looking to use those properties first... they certainly do work much faster. Unfortunately, for this problem we have to cancel out the third root in the denominator by creating a third power down there due to the different bases.
Just like we say "x" instead of "1*x" for simplicity, the same is true for the unwritten power in our numerator. We say "7" even though it's really "7^1" Now, you're right, since we are dividing expressions with the same base, we keep the base and subtract the exponents. Here, that means that unwritten 1 minus the 1/3 we have for a power in the denominator, and the base stays at 7... that's where the 2/3 comes from. It makes a lot more sense if you think about it with more casual language. Let's say we have (n^6)/(n^4). Although more wordy, it makes sense to think of this as saying "I have 6 'n's multiplied together, and I'm dividing away 4 of those 'n's multiplied together...Oh, that means there's only 2 'n's multiplied together left... n^2" Hope this helps!
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Thank you so much. I have been quarantined so I can’t be in school . You saved me from a meltdown because the practice problems that my teacher gave me look nothing like what I learned. You’re a good teacher!
Thanks for the vid but it will literally take a miracle for me to get this 🙃
This is not hard it’s abt remembering your properties in my opinion
@@noahgonzalez4111 How did he get two in problem 6 ?
At 17:12 why don’t you add the exponents of 7 and 2 because don’t all numbers have an exponent of 1 and you add exponents when multiplying.
This is a good question, as one of our tactics in simplifying is to combine whatever we can. The reason we don't add exponents here is for 2 reasons... First, we can only do the *add the exponents* trick if we are multiplying together two factors that have the same base. Since 7^(1/3) and 2^1 have different bases, 7 and 2, that option isn't available. Secondly, when faced with division like we see in the fraction, the property would have us *subtract the exponents* to simplify, but again, only if those terms have the same base.
It's great that you're looking to use those properties first... they certainly do work much faster. Unfortunately, for this problem we have to cancel out the third root in the denominator by creating a third power down there due to the different bases.
4:43 why is it 2/3 if you're subtracting?
Just like we say "x" instead of "1*x" for simplicity, the same is true for the unwritten power in our numerator. We say "7" even though it's really "7^1"
Now, you're right, since we are dividing expressions with the same base, we keep the base and subtract the exponents. Here, that means that unwritten 1 minus the 1/3 we have for a power in the denominator, and the base stays at 7... that's where the 2/3 comes from.
It makes a lot more sense if you think about it with more casual language. Let's say we have (n^6)/(n^4). Although more wordy, it makes sense to think of this as saying "I have 6 'n's multiplied together, and I'm dividing away 4 of those 'n's multiplied together...Oh, that means there's only 2 'n's multiplied together left... n^2"
Hope this helps!
This is great. Thanks man
thanks
Good vid but this is actually beyond my comprehension level