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

  • question_answer
    If \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\], find the value of \[{{x}^{2}}\].

    A)  \[{{\left( \frac{4}{3} \right)}^{12}}\]                     

    B)  \[{{\left( \frac{2}{3} \right)}^{12}}\]         

    C)  \[{{\left( \frac{3}{2} \right)}^{12}}\]         

    D)         \[{{\left( \frac{3}{4} \right)}^{12}}\]         

    Correct Answer: B

    Solution :

    We have, \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\]             \[={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{3}{2} \right)}^{4}}={{\left( \frac{3}{2} \right)}^{6}}\] So, \[{{x}^{-2}}={{\left( {{\left( \frac{3}{2} \right)}^{6}} \right)}^{-2}}={{\left( \frac{3}{2} \right)}^{-12}}={{\left( \frac{2}{3} \right)}^{12}}\]


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