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Math Help - Double Exponents

  1. #1
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    Double Exponents

    I want to find 2^3^(k+1) in terms of k.
    I think that 2^3^(k+1)=(2^3^k)^3 is true, however I don't understand how to manipulate these double exponents
    I have looked for 'rules' unsuccessfully, can anyone enlighten me?
    Also if someone could please show me how to write double exponents in latex that would be great.
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  2. #2
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    Re: Double Exponents

    Hello, dnftp!

    I have two issues with this problem . . .


    I want to find 2^3^(k+1) in terms of k.

    [1] The expression is already in terms of k.
    . . .So what are they asking us to do?

    [2] There are two ways to read this problem.

    . . . \displaystyle(2^3)^{k+1}\:\text{ and }\;2^{3^{k+1}}
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  3. #3
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    Re: Double Exponents

    Hi, Soroban
    Yes I worded the question badly.
    I want to use induction to prove a statement.
    I have been given 2^{3^{k}}, I apply the inductive step k + 1, to get 2^{3^{k+1}}, and want to rewrite this without k+1, just k.
    What I had previously written was 2^{3^{k+1}} = (2^{3^{k}})^3
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  4. #4
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    Re: Double Exponents

    There is some confusion in writing the question. I do not find a statement that you want to prove by Mathematical Induction. Please recheck and post it again.
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  5. #5
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    Re: Double Exponents

    I don't need help with the induction, I was trying to give an indication of why I was asking.
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