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9th Class Mathematics Number System and its Operations Question Bank Number System

  • question_answer
    The largest among the numbers \[{{\mathbf{2}}^{\mathbf{250}}}\mathbf{,}{{\mathbf{3}}^{\mathbf{150}}}\mathbf{,}{{\mathbf{5}}^{\mathbf{100}}}\] and \[{{\mathbf{4}}^{\mathbf{200}}}\] is

    A)  \[{{4}^{200}}\]      

    B)  5100              

    C)  2250                             

    D)  2150

    Correct Answer: A

    Solution :

    (a): (1) \[{{2}^{250}}={{\left( {{2}^{5}} \right)}^{50}}={{32}^{50}};\] (2) \[{{3}^{150}}={{\left( {{3}^{3}} \right)}^{50}}={{\left( 27 \right)}^{50}}\] (3) \[{{3}^{100}}={{\left( {{5}^{2}} \right)}^{50}}={{\left( 25 \right)}^{50}};\] (4) \[{{4}^{200}}={{\left( {{4}^{4}} \right)}^{50}}={{\left( 256 \right)}^{50}}\] Hence, \[{{4}^{200}}\] is the greatest.               


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