A) \[{{\left( \frac{4}{3} \right)}^{12}}\]
B) \[{{\left( \frac{2}{3} \right)}^{12}}\]
C) \[{{\left( \frac{3}{2} \right)}^{12}}\]
D) \[{{\left( \frac{3}{4} \right)}^{12}}\]
Correct Answer: B
Solution :
We have, \[x={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{2}{3} \right)}^{-4}}\] \[={{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{3}{2} \right)}^{4}}={{\left( \frac{3}{2} \right)}^{6}}\] So, \[{{x}^{-2}}={{\left( {{\left( \frac{3}{2} \right)}^{6}} \right)}^{-2}}={{\left( \frac{3}{2} \right)}^{-12}}={{\left( \frac{2}{3} \right)}^{12}}\]You need to login to perform this action.
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