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Math Help - x^{a+b}=x^ax^b

  1. #1
    MHF Contributor
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    x^{a+b}=x^ax^b

    G is a group and x\in G and a,b\in\mathbb{N}.

    Prove x^{a+b}=x^ax^b

    I don't see how to show this. Multiplying by the inverse would just use the property I have to prove.
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  2. #2
    A Plied Mathematician
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    Re: x^{a+b}=x^ax^b

    Could you just write this:

    x^{a+b}=\underbrace{x\cdot x\cdot...\cdot x}_{a+b\text{ times}}=\underbrace{x\cdot x\cdot...\cdot x}_{a\text{ times}}\cdot\underbrace{x\cdot x\cdot...\cdot x}_{b\text{ times}}=x^{a}x^{b},

    and claim you're done? I would definitely claim that there isn't much to show here. The proof can't be that complex.
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  3. #3
    MHF Contributor

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    Re: x^{a+b}=x^ax^b

    More "rigorously", prove it by induction on a and b.
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