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Math Help - Solving problems.

  1. #1
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    Solving problems.

    Porve that b^(r+s) = b^r * b^s, r and s are rationals.
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let r=\frac{m}{n}, \ s=\frac{p}{q}, \ m,n,p,q\in\mathbb{N}, \ n,q\neq 0

    Then b^{r+s}=b^{\displaystyle\frac{m}{n}+\frac{p}{q}}=b  ^{\displaystyle\frac{mq+np}{nq}}=

    =\displaystyle\sqrt[nq]{b^{mq+np}}=\sqrt[nq]{b^{mq}b^{np}}=

    =\sqrt[nq]{b^{mq}}\cdot\sqrt[nq]{b^{np}}=b^{\frac{mq}{nq}}\cdot b^{\frac{np}{nq}}=b^{\frac{m}{n}}\cdot b^{\frac{p}{q}}=b^r\cdot b^s

    In a similar way you can prove if r or s or both are negative.
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