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Math Help - Very large exponent

  1. #1
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    Very large exponent

    I need help defining the following very large exponent:

    10,000 ^ 13,766,400

    No doubt, this number is astronomical...but surely (hopefully) it can be expressed with scientific notation. The calculation has maxed out my TI-83 as well as any online calculator designed to handle large calculations. I do not consider myself to be mathematically inclined, so I have no way of knowing whether or not I am asking for something absurd. I appreciate any help in this matter.
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    Quote Originally Posted by cerpintaxt33 View Post
    I need help defining the following very large exponent:

    10,000 ^ 13,766,400
    Here is an example: (10,000)^{321}=(10^4)^{321}=(10)^{1284}
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  3. #3
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    Quote Originally Posted by cerpintaxt33 View Post
    I need help defining the following very large exponent:

    10,000 ^ 13,766,400

    No doubt, this number is astronomical...but surely (hopefully) it can be expressed with scientific notation. The calculation has maxed out my TI-83 as well as any online calculator designed to handle large calculations. I do not consider myself to be mathematically inclined, so I have no way of knowing whether or not I am asking for something absurd. I appreciate any help in this matter.
    In scientific notation it is: 1 \times 10^{13,766,404}

    You should not need a calculator for this just the definition of scientific notation and the laws of exponents.

    (most calculators and computer languages are limited to decimal exponents of 3 or less digits, some not being able to handle even 3 digits)

    CB
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  4. #4
    Member mfetch22's Avatar
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    Quote Originally Posted by cerpintaxt33 View Post
    I need help defining the following very large exponent:

    10,000 ^ 13,766,400

    No doubt, this number is astronomical...but surely (hopefully) it can be expressed with scientific notation. The calculation has maxed out my TI-83 as well as any online calculator designed to handle large calculations. I do not consider myself to be mathematically inclined, so I have no way of knowing whether or not I am asking for something absurd. I appreciate any help in this matter.

    Note that 10^4 = 10,000

    So, since sicientfic notation is expressed in base 10, and the number in front of the 10 in this case is 1 we have:

    (10,000)^{13,766,400} = (10^4)^{13,766,400}

    And an exponant to an exponant is simply the exponants multiplied together so we have:

    (10,000)^{13,766,400} = 10^{4*13,766,400} = 10^{55,065,600}

    And since its multiplied by 1 we have:

    1X 10^{55,065,600}
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    Thanks, I appreciate it. Any idea how many digits this number would be?
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  6. #6
    Member mfetch22's Avatar
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    Quote Originally Posted by cerpintaxt33 View Post
    Thanks, I appreciate it. Any idea how many digits this number would be?
    Well since 10^n adds n-1 zeros to 10 (and thus n-1 digits ), and becuause 10 already adds two digits, I beleive that this number would have 55,065,601 digits
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