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Math Help - Zero and 1st Exponents

  1. #1
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    Smile Zero and 1st Exponents

    I know that any number raised to the zero power is 1.
    I also know that any number raised to the 1st power is the number itself.

    Sample A:

    Let x = a number

    Then x^(0) = 1....Wny is this the case?

    Sample B:

    Let y = a number

    Then y^(1) = y....Why is this the case?

    Teachers never explain this in terms that students can understand.

    How about you?

    How would you EASILY teach the above concepts in a classroom?

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  2. #2
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    Because it is defined this way. Return to the definition of exponents in your textbook or read here:
    Exponentiation - Wikipedia, the free encyclopedia
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  3. #3
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    Back in the day when my teacher taught me it, he told us to put it in the calculator and see what we get.

    The way you would explain B is: y^2=y*y, y^1=y

    Those two are just a matter of memorizing (which isn't that hard of a grueling task).
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  4. #4
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    Quote Originally Posted by magentarita View Post
    I know that any number raised to the zero power is 1.
    I also know that any number raised to the 1st power is the number itself.

    Sample A:

    Let x = a number

    Then x^(0) = 1....Wny is this the case?

    Sample B:

    Let y = a number

    Then y^(1) = y....Why is this the case?

    Teachers never explain this in terms that students can understand.

    How about you?

    How would you EASILY teach the above concepts in a classroom?
    Not EVERY number taken to the power of 0 equals 1...

    0^0 is undefined...
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  5. #5
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    This is my point.....

    Quote Originally Posted by Chop Suey View Post
    Because it is defined this way. Return to the definition of exponents in your textbook or read here:
    Exponentiation - Wikipedia, the free encyclopedia
    My point is that textbooks definitions are not clear and not easy to grasp. I am looking for an easy explanation not math jargon. If I want math jargon, I simply read my textbook which does not sense.
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  6. #6
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    memory games

    Quote Originally Posted by nic42991 View Post
    Back in the day when my teacher taught me it, he told us to put it in the calculator and see what we get.

    The way you would explain B is: y^2=y*y, y^1=y

    Those two are just a matter of memorizing (which isn't that hard of a grueling task).
    This is my point. To memorize the rules is fine but to know exactly why something has been established can help students see the bigger picture.
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  7. #7
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    again...

    Quote Originally Posted by Prove It View Post
    Not EVERY number taken to the power of 0 equals 1...

    0^0 is undefined...
    We all know that 0^(0) does not exist but why????

    See my point?

    We can memorize many rules but knowing the [why] of things makes all things clear.
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  8. #8
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    Quote Originally Posted by magentarita View Post
    This is my point. To memorize the rules is fine but to know exactly why something has been established can help students see the bigger picture.
    The only bigger picture most students want is a 42" widescreen plasma TV.
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  9. #9
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    oh....

    Quote Originally Posted by mr fantastic View Post
    The only bigger picture most students want is a 42" widescreen plasma TV.
    I guess education is more about memory than anything else.
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  10. #10
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    Quote Originally Posted by magentarita View Post
    I guess education is more about memory than anything else.
    Most students think this. And, unfortunately, the exams that they're given usually perpetuate and reinforce this viewpoint.

    There's always an uproar when an examination has questions different to the ones that have appeared on previous examinations. The usual objection is that this is unfair because they hadn't learned that sort of question. At this point I usually remark that my heart bleeds and reach for my violin.
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  11. #11
    Junior Member shinhidora's Avatar
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    x^0 = 1

    If you have no power at all (so 0 power), you're still that one ( 1 ) powerless being

    Exception: If you have no value at all ( 0 ) and no power at all, how would you be defined? Not!

    y^1 = y

    If your power is 1, no matter how much you jump around and stuff, you'll always be yourself

    Et voila!
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  12. #12
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    Quote Originally Posted by magentarita View Post
    I know that any number raised to the zero power is 1.
    I also know that any number raised to the 1st power is the number itself.

    Sample A:

    Let x = a number

    Then x^(0) = 1....Wny is this the case?

    You probably know that anything to the 0 power is 1. But now you can see why. Consider x^0.
    By the division rule, you know that


    \frac{x^3}{x^3}=x^{3-3}=x^0.


    But anything divided by itself is 1, so \frac{x^3}{x^3} = 1. Things that are equal to the same thing are equal to each other: if \frac{x^3}{x^3} is equal to both 1 and x^0, then 1 must equal x^0. Symbolically,

    x^0=x^{3-3}=\frac{x^3}{x^3}=1

    There’s one restriction. You saw that we had to create a fraction to figure out x^0. But division by 0 is not allowed, so our evaluation works for anything to the 0 power except zero itself.

    Quote Originally Posted by magentarita View Post
    Sample B:



    Let y = a number

    Then y^(1) = y....Why is this the case?

    Teachers never explain this in terms that students can understand.

    How about you?

    How would you EASILY teach the above concepts in a classroom?
    There’s nothing mysterious! An exponent is simply shorthand for multiplying that number of identical factors. So 4^3 is the same as (4)(4)(4), three identical factors of 4. And y^3 is just three factors of y, (y)(y)(y). In a similar fashion, y^1 means y is used as a factor 1 time, and since 1 is always a factor of any number we have:


    {\color{red}y^1=1 \cdot y = y}
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  13. #13
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    great

    Quote Originally Posted by masters View Post
    You probably know that anything to the 0 power is 1. But now you can see why. Consider x^0.
    By the division rule, you know that


    \frac{x^3}{x^3}=x^{3-3}=x^0.


    But anything divided by itself is 1, so \frac{x^3}{x^3} = 1. Things that are equal to the same thing are equal to each other: if \frac{x^3}{x^3} is equal to both 1 and x^0, then 1 must equal x^0. Symbolically,

    x^0=x^{3-3}=\frac{x^3}{x^3}=1

    There’s one restriction. You saw that we had to create a fraction to figure out x^0. But division by 0 is not allowed, so our evaluation works for anything to the 0 power except zero itself.



    There’s nothing mysterious! An exponent is simply shorthand for multiplying that number of identical factors. So 4^3 is the same as (4)(4)(4), three identical factors of 4. And y^3 is just three factors of y, (y)(y)(y). In a similar fashion, y^1 means y is used as a factor 1 time, and since 1 is always a factor of any number we have:


    {\color{red}y^1=1 \cdot y = y}
    Excellent reply!
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  14. #14
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    cute

    Quote Originally Posted by shinhidora View Post
    x^0 = 1

    If you have no power at all (so 0 power), you're still that one ( 1 ) powerless being

    Exception: If you have no value at all ( 0 ) and no power at all, how would you be defined? Not!

    y^1 = y

    If your power is 1, no matter how much you jump around and stuff, you'll always be yourself

    Et voila!
    A cute way of looking at this stuff.
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