6th Class Mathematics Exponents and Power Question Bank Exponent and Powers

  • question_answer The value of\[{{\left( \frac{8}{125} \right)}^{\frac{-4}{3}}}\]

    A)  \[\frac{625}{16}\]                           

    B) \[\frac{125}{16}\]

    C) \[\frac{16}{25}\]                                              

    D) \[\frac{-625}{16}\]

    Correct Answer: A

    Solution :

    \[{{\left( \frac{8}{125} \right)}^{{}^{-4}/{}_{3}}}={{\left( \frac{{{2}^{3}}}{{{5}^{3}}} \right)}^{{}^{-4}/{}_{3}}}={{\left[ \frac{2}{5} \right]}^{\left( {}^{-4}/{}_{3} \right)\times 3}}\] \[={{\left( \frac{2}{5} \right)}^{-4}}={{\left( \frac{5}{2} \right)}^{4}}=\frac{{{5}^{4}}}{{{2}^{4}}}=\frac{625}{16}\]

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