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

  • question_answer
    The value of \[\frac{{{2}^{2001}}+{{2}^{1999}}}{{{2}^{2000}}-{{2}^{1998}}}\], is _____.

    A)  2                                

    B)  \[10/3\]           

    C)  \[{{2}^{1000}}+1\]           

    D)         \[\text{10}\]   

    Correct Answer: B

    Solution :

    \[\frac{{{2}^{2001}}+{{2}^{1999}}}{{{2}^{2000}}-{{2}^{1998}}}=\frac{{{2}^{1999}}({{2}^{2}}+1)}{{{2}^{1998}}({{2}^{2}}-1)}\] \[={{2}^{1999-1998}}\left( \frac{4+1}{4-1} \right)\]        \[\left[ \because \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \right]\] \[=2\left( \frac{5}{3} \right)=\frac{10}{3}\]


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