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Math Help - Exponent Exponents?

  1. #1
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    Exponent Exponents?

    Please could somebody explain to me what x^{y^z} equals. I know that when the second power is in brackets the powers multiply, e.g. (x^y)^z = x^{yz} but I do not know what to do when the indices are not separated by brackets.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Bruce View Post
    Please could somebody explain to me what x^{y^z} equals. I know that when the second power is in brackets the powers multiply, e.g. (x^y)^z = x^{yz} but I do not know what to do when the indices are not separated by brackets.
    Hi Bruce,

    x^{y^z} means you find y^z first, then you raise x to that exponent value.

    Example:

    2^{3^2}=2^9=512

    That's different from:

    (2^3)^2=8^2=64

    Does that help?
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  3. #3
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    That is great, thanks.

    To check my understanding, is 3^{2^{3^2}}

    3^{2^9}
    3^{512}

    So you work down finding each single power first from the top.
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  4. #4
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    Quote Originally Posted by Bruce View Post
    That is great, thanks.

    To check my understanding, is 3^{2^{3^2}}

    3^{2^9}

    3^{512}

    So you work down finding each single power first from the top.
    Yes, Bruce. That is correct. BTW, that's a huge number.
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