Dividing numbers with exponents and powers











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Can someone please help me simplify the below problem. I am trying to help my niece



$${24C^4 over 4C^{12}}$$



I believe that the simplified answer is $6/C^8$ because $4$ goes into $24$ $6$ times and $6$ remains as the numerator. Also, you need to subtract $4$ from $C^4$ which becomes $1$ and subtract $4$ from $C^{12}$ and it equals $C^8$. however my niece thinks it is: $1/(6C^8)$. what is the correct answer?










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  • You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
    – Andrew Li
    yesterday












  • What is the "communicative property"?
    – NickD
    22 hours ago










  • @NickD I think autocorrect got me. Commutative.
    – Andrew Li
    19 hours ago















up vote
1
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Can someone please help me simplify the below problem. I am trying to help my niece



$${24C^4 over 4C^{12}}$$



I believe that the simplified answer is $6/C^8$ because $4$ goes into $24$ $6$ times and $6$ remains as the numerator. Also, you need to subtract $4$ from $C^4$ which becomes $1$ and subtract $4$ from $C^{12}$ and it equals $C^8$. however my niece thinks it is: $1/(6C^8)$. what is the correct answer?










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  • You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
    – Andrew Li
    yesterday












  • What is the "communicative property"?
    – NickD
    22 hours ago










  • @NickD I think autocorrect got me. Commutative.
    – Andrew Li
    19 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Can someone please help me simplify the below problem. I am trying to help my niece



$${24C^4 over 4C^{12}}$$



I believe that the simplified answer is $6/C^8$ because $4$ goes into $24$ $6$ times and $6$ remains as the numerator. Also, you need to subtract $4$ from $C^4$ which becomes $1$ and subtract $4$ from $C^{12}$ and it equals $C^8$. however my niece thinks it is: $1/(6C^8)$. what is the correct answer?










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Can someone please help me simplify the below problem. I am trying to help my niece



$${24C^4 over 4C^{12}}$$



I believe that the simplified answer is $6/C^8$ because $4$ goes into $24$ $6$ times and $6$ remains as the numerator. Also, you need to subtract $4$ from $C^4$ which becomes $1$ and subtract $4$ from $C^{12}$ and it equals $C^8$. however my niece thinks it is: $1/(6C^8)$. what is the correct answer?







algebra-precalculus






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  • You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
    – Andrew Li
    yesterday












  • What is the "communicative property"?
    – NickD
    22 hours ago










  • @NickD I think autocorrect got me. Commutative.
    – Andrew Li
    19 hours ago


















  • You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
    – Andrew Li
    yesterday












  • What is the "communicative property"?
    – NickD
    22 hours ago










  • @NickD I think autocorrect got me. Commutative.
    – Andrew Li
    19 hours ago
















You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
– Andrew Li
yesterday






You are correct. Do you know why your niece thinks it's $1/C^8$? You could use the communicative property to rewrite it as $24/4 cdot C^4/C^{12}$ to make it more explicit.
– Andrew Li
yesterday














What is the "communicative property"?
– NickD
22 hours ago




What is the "communicative property"?
– NickD
22 hours ago












@NickD I think autocorrect got me. Commutative.
– Andrew Li
19 hours ago




@NickD I think autocorrect got me. Commutative.
– Andrew Li
19 hours ago










2 Answers
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One approach I've used for someone beginning to work with this type of situation is the following, although I'd probably replace it with something similar and simpler, such as $frac{24C^2}{4C^5},$ to actually illustrate the idea.



$$ frac{24C^4}{4C^{12}} ; = ; frac{24 cdot C^4}{4 cdot C^{12}} ; = ; frac{24}{4} cdot frac{C^4}{C^{12}} $$



$$ = ; ; frac{24}{4} cdot frac{C cdot C cdot C cdot C cdot 1 cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1}{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C} $$



$$ = ;; frac{24}{4} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



$$ = ;; frac{6}{1} cdot 1 cdot 1 cdot 1 cdot 1 cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



$$ = ;; frac{6}{1} cdot frac{1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 }{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C}$$



$$ = ;; frac{6}{1} cdot frac{1}{C^8} ;; = ;; frac{6}{C^8} $$



What you want to do is go over several elaborate expansions like this and let the student discover the shortcuts that can be taken, and then when the student is comfortable with simple things like this (integer times a letter to a positive integer power, divided by an integer times a letter to a positive integer power), begin branching out to things like $frac{24x^3y^5}{6x^2y^8}.$ All this should not take more than 5 to 15 minutes, after which you can begin talking about the relevance of the laws of exponents to the shortcuts the student has observed, as well as mixing in things like $C^3 cdot C^4 = (CCC)cdot (CCCC) = CCCCCCC = C^{3+4}$ $(3;C$'s followed by $4;C$'s is $7;C$'s), if this had not already been done at some previous time.






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Yes you are correct. The simplified answer is $frac{6}{C^8}$.






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    2 Answers
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    One approach I've used for someone beginning to work with this type of situation is the following, although I'd probably replace it with something similar and simpler, such as $frac{24C^2}{4C^5},$ to actually illustrate the idea.



    $$ frac{24C^4}{4C^{12}} ; = ; frac{24 cdot C^4}{4 cdot C^{12}} ; = ; frac{24}{4} cdot frac{C^4}{C^{12}} $$



    $$ = ; ; frac{24}{4} cdot frac{C cdot C cdot C cdot C cdot 1 cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1}{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C} $$



    $$ = ;; frac{24}{4} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot 1 cdot 1 cdot 1 cdot 1 cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot frac{1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 }{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C}$$



    $$ = ;; frac{6}{1} cdot frac{1}{C^8} ;; = ;; frac{6}{C^8} $$



    What you want to do is go over several elaborate expansions like this and let the student discover the shortcuts that can be taken, and then when the student is comfortable with simple things like this (integer times a letter to a positive integer power, divided by an integer times a letter to a positive integer power), begin branching out to things like $frac{24x^3y^5}{6x^2y^8}.$ All this should not take more than 5 to 15 minutes, after which you can begin talking about the relevance of the laws of exponents to the shortcuts the student has observed, as well as mixing in things like $C^3 cdot C^4 = (CCC)cdot (CCCC) = CCCCCCC = C^{3+4}$ $(3;C$'s followed by $4;C$'s is $7;C$'s), if this had not already been done at some previous time.






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    • +1 for Exceptional effort from exceptional person.
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      yesterday















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    One approach I've used for someone beginning to work with this type of situation is the following, although I'd probably replace it with something similar and simpler, such as $frac{24C^2}{4C^5},$ to actually illustrate the idea.



    $$ frac{24C^4}{4C^{12}} ; = ; frac{24 cdot C^4}{4 cdot C^{12}} ; = ; frac{24}{4} cdot frac{C^4}{C^{12}} $$



    $$ = ; ; frac{24}{4} cdot frac{C cdot C cdot C cdot C cdot 1 cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1}{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C} $$



    $$ = ;; frac{24}{4} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot 1 cdot 1 cdot 1 cdot 1 cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot frac{1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 }{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C}$$



    $$ = ;; frac{6}{1} cdot frac{1}{C^8} ;; = ;; frac{6}{C^8} $$



    What you want to do is go over several elaborate expansions like this and let the student discover the shortcuts that can be taken, and then when the student is comfortable with simple things like this (integer times a letter to a positive integer power, divided by an integer times a letter to a positive integer power), begin branching out to things like $frac{24x^3y^5}{6x^2y^8}.$ All this should not take more than 5 to 15 minutes, after which you can begin talking about the relevance of the laws of exponents to the shortcuts the student has observed, as well as mixing in things like $C^3 cdot C^4 = (CCC)cdot (CCCC) = CCCCCCC = C^{3+4}$ $(3;C$'s followed by $4;C$'s is $7;C$'s), if this had not already been done at some previous time.






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    • +1 for Exceptional effort from exceptional person.
      – NoChance
      yesterday













    up vote
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    down vote










    up vote
    1
    down vote









    One approach I've used for someone beginning to work with this type of situation is the following, although I'd probably replace it with something similar and simpler, such as $frac{24C^2}{4C^5},$ to actually illustrate the idea.



    $$ frac{24C^4}{4C^{12}} ; = ; frac{24 cdot C^4}{4 cdot C^{12}} ; = ; frac{24}{4} cdot frac{C^4}{C^{12}} $$



    $$ = ; ; frac{24}{4} cdot frac{C cdot C cdot C cdot C cdot 1 cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1}{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C} $$



    $$ = ;; frac{24}{4} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot 1 cdot 1 cdot 1 cdot 1 cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot frac{1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 }{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C}$$



    $$ = ;; frac{6}{1} cdot frac{1}{C^8} ;; = ;; frac{6}{C^8} $$



    What you want to do is go over several elaborate expansions like this and let the student discover the shortcuts that can be taken, and then when the student is comfortable with simple things like this (integer times a letter to a positive integer power, divided by an integer times a letter to a positive integer power), begin branching out to things like $frac{24x^3y^5}{6x^2y^8}.$ All this should not take more than 5 to 15 minutes, after which you can begin talking about the relevance of the laws of exponents to the shortcuts the student has observed, as well as mixing in things like $C^3 cdot C^4 = (CCC)cdot (CCCC) = CCCCCCC = C^{3+4}$ $(3;C$'s followed by $4;C$'s is $7;C$'s), if this had not already been done at some previous time.






    share|cite|improve this answer












    One approach I've used for someone beginning to work with this type of situation is the following, although I'd probably replace it with something similar and simpler, such as $frac{24C^2}{4C^5},$ to actually illustrate the idea.



    $$ frac{24C^4}{4C^{12}} ; = ; frac{24 cdot C^4}{4 cdot C^{12}} ; = ; frac{24}{4} cdot frac{C^4}{C^{12}} $$



    $$ = ; ; frac{24}{4} cdot frac{C cdot C cdot C cdot C cdot 1 cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1cdot 1}{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C cdot C} $$



    $$ = ;; frac{24}{4} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{C}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot 1 cdot 1 cdot 1 cdot 1 cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} cdot frac{1}{C} $$



    $$ = ;; frac{6}{1} cdot frac{1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 cdot 1 }{C cdot C cdot C cdot C cdot C cdot C cdot C cdot C}$$



    $$ = ;; frac{6}{1} cdot frac{1}{C^8} ;; = ;; frac{6}{C^8} $$



    What you want to do is go over several elaborate expansions like this and let the student discover the shortcuts that can be taken, and then when the student is comfortable with simple things like this (integer times a letter to a positive integer power, divided by an integer times a letter to a positive integer power), begin branching out to things like $frac{24x^3y^5}{6x^2y^8}.$ All this should not take more than 5 to 15 minutes, after which you can begin talking about the relevance of the laws of exponents to the shortcuts the student has observed, as well as mixing in things like $C^3 cdot C^4 = (CCC)cdot (CCCC) = CCCCCCC = C^{3+4}$ $(3;C$'s followed by $4;C$'s is $7;C$'s), if this had not already been done at some previous time.







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    answered yesterday









    Dave L. Renfro

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    • +1 for Exceptional effort from exceptional person.
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    +1 for Exceptional effort from exceptional person.
    – NoChance
    yesterday




    +1 for Exceptional effort from exceptional person.
    – NoChance
    yesterday










    up vote
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    Yes you are correct. The simplified answer is $frac{6}{C^8}$.






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      Yes you are correct. The simplified answer is $frac{6}{C^8}$.






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        up vote
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        Yes you are correct. The simplified answer is $frac{6}{C^8}$.






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        Yes you are correct. The simplified answer is $frac{6}{C^8}$.







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        answered yesterday









        Avinash N

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