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7th Class Mathematics Exponents and Power Question Bank Exponents and Powers

  • question_answer
    Mr Gupta asked two of his students to solve the expression \[{{\left( \frac{9{{a}^{3}}{{b}^{-8}}}{81{{a}^{-5}}{{b}^{2}}} \right)}^{-\frac{1}{2}}}\]and write the answer on blackboard. Aryan wrote the answer as \[3{{a}^{-4}}{{b}^{5}}\] whereas Ayan wrote the answer as \[\frac{3{{b}^{5}}}{{{a}^{4}}}\].  Who wrote the correct answer?

    A)  Aryan

    B)  Ayan

    C)  Both of them

    D)  None of these

    Correct Answer: C

    Solution :

    We have, \[{{\left( \frac{9{{a}^{3}}{{b}^{-8}}}{81{{a}^{-5}}{{b}^{2}}} \right)}^{-\frac{1}{2}}}={{\left( \frac{81{{a}^{-5}}{{b}^{2}}}{9{{a}^{3}}{{b}^{-8}}} \right)}^{\frac{1}{2}}}\] \[={{\left( 9{{a}^{-5}}{{a}^{-3}}{{b}^{2}}{{b}^{6}} \right)}^{\frac{1}{2}}}\]      \[={{\left( 9{{a}^{-8}}{{b}^{10}} \right)}^{\frac{1}{2}}}=3\,{{a}^{-4}}{{b}^{5}}\]


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