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Math Help - Power Proof

  1. #1
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    Power Proof

    Hey all, I'd really appreciate some help with the following proof about powers:

    (b^m)^k = b^(mk)

    Power is defined in the following way. Let b be a fixed integer. We define b^k for all integers k >= 0 by:

    b^0 := 1

    Assuming b^n defined, let b^(n+1) := b^n * b


    Thanks a lot!
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  2. #2
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    Quote Originally Posted by jstarks44444 View Post
    Hey all, I'd really appreciate some help with the following proof about powers:

    (b^m)^k = b^(mk)

    Power is defined in the following way. Let b be a fixed integer. We define b^k for all integers k >= 0 by:

    b^0 := 1

    Assuming b^n defined, let b^(n+1) := b^n * b


    Thanks a lot!
    Well pf. by induction.

    Base case k=0

    (b^m)^0=1 by definition.

    Assume the cases  k is true

    (b^m)^k=b^{mk}

    Now show k \implies k+1

    (b^{m})^{k+1}=(b^m)^k\cdot (b^m)^1 by your assumption

    Now by the induction hypothesis we get
    b^{mk}\codt b^m=b^{mk+m}=b^{m(k+1)}
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