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Math Help - Simple Algebraic Manipulation

  1. #1
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    Simple Algebraic Manipulation

    Can somebody explain the rules of algebra so that the following expression makes sense:

    2^{2 \cdot 2^m}+1 =\left(2^{2^m}\right)^2+1

    I thought that \left(2^{2^m}\right)^2+1 =4^{ \cdot 4^(m^2)}+1 but apparently thats wrong.
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  2. #2
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    Quote Originally Posted by 1337h4x View Post
    Can somebody explain the rules of algebra so that the following expression makes sense:

    2^{2 \cdot 2^m}+1 =\left(2^{2^m}\right)^2+1

    I thought that \left(2^{2^m}\right)^2+1 =4^{ \cdot 4^(m^2)}+1 but apparently thats wrong.
    The rule is (a^l)^k= a^{lk}.

    Now choose a = 2, l = 2 and k = 2^m...
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    The rule is (a^l)^k= a^{lk}.

    Now choose a = 2, l = 2 and k = 2^m...
    I'm not sure how we get from my form of \left(a^{b^m}\right)^k to (a^l)^k
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  4. #4
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    Quote Originally Posted by 1337h4x View Post
    Can somebody explain the rules of algebra so that the following expression makes sense:



    I thought that but apparently thats wrong.
    Hi 1337h4x,

    This is what it looks like to me.

    2^{2 \cdot 2^m}+1=\left(2^{2^m}\right)^2

    2^{2^1 \cdot 2^m}+1=2^{2^m \cdot 2}

    2^{2^{m+1}}+1=2^{2^{m+1}}+1

    The properties you use is the power of a power rule and the product of powers rule.

    (a^m)^n=a^{mn}

    a^m \cdot a^n=a^{m+n}
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