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8th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    When simplified, \[{{\text{(}{{\text{x}}^{-1}}+{{y}^{-1}})}^{-1}}\] is equal to_____.

    A)  \[x+y\]           

    B)         \[\frac{xy}{x+y}\]    

    C)  \[xy\]              

    D)         \[\frac{1}{xy}\]         

    Correct Answer: B

    Solution :

    \[:{{({{x}^{-1}}+{{y}^{-1}})}^{-1}}={{\left( \frac{1}{x}+\frac{1}{y} \right)}^{-1}}={{\left( \frac{x+y}{xy} \right)}^{-1}}\]                         \[=\frac{xy}{x+y}\left[ \because {{a}^{-n}}=\frac{1}{{{a}^{n}}} \right]\]


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