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

  • question_answer
    What is the value of \[{{\left( \frac{-1}{216} \right)}^{-2/3}}\]?

    A)  \[36\]                                  

    B)  \[-36\]                

    C)  \[\frac{1}{36}\]               

    D)  \[\frac{-1}{36}\]

    Correct Answer: A

    Solution :

    Clearly \[{{\left( \frac{-1}{216} \right)}^{\frac{-2}{3}}}={{\left[ {{\left( \frac{-1}{6} \right)}^{3}} \right]}^{\frac{-2}{3}}}\]                 \[={{\left( \frac{-1}{6} \right)}^{3\times \frac{-2}{3}}}={{\left( \frac{-1}{6} \right)}^{-2}}\]                 \[=\frac{1}{{{(-1/6)}^{2}}}=\frac{1}{(1/36)}=36\]


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