A) \[\frac{625}{16}\]
B) \[\frac{125}{16}\]
C) \[\frac{16}{25}\]
D) \[\frac{-625}{16}\]
Correct Answer: A
Solution :
(a) \[{{\left( \frac{8}{125} \right)}^{^{{}^{-4}/{}_{3}}}}={{\left( \frac{{{2}^{3}}}{{{5}^{3}}} \right)}^{^{{}^{-4}/{}_{3}}}}={{\left[ \frac{2}{5} \right]}^{\left( {}^{-4}/{}_{3} \right)\times 3}}\] \[={{\left( \frac{2}{5} \right)}^{-4}}={{\left( \frac{5}{2} \right)}^{4}}=\frac{{{5}^{4}}}{{{2}^{4}}}=\frac{625}{16}\]
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