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

  • question_answer
    Find the value of m in the expression \[\frac{{{\left( 16 \right)}^{2m+1}}{{\left( 64 \right)}^{5}}}{{{\left( 256 \right)}^{2}}\times 4}={{\left( 256 \right)}^{3m}}\]

    A)  1          

    B)  0            

    C)  4                                

    D)  5

    Correct Answer: A

    Solution :

    (a): \[\frac{{{16}^{(2m+1)}}\times {{64}^{5}}}{{{256}^{2}}\times 4}=\frac{{{16}^{(2m+1)}}\times {{\left( {{16}^{3/2}} \right)}^{5}}}{{{(16)}^{4}}\times 4}\].             \[=\frac{{{16}^{(2m+1)}}\times {{64}^{\frac{7}{2}}}}{4}=\frac{{{16}^{(2m+\frac{9}{2})}}}{4};RHS={{(16)}^{6m}}\] Since LHS = RHS;             \[\therefore {{16}^{2}}^{m+4}={{16}^{6m}}\Rightarrow 2m+4=6m\Rightarrow m=1\]


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