A) \[{{\left[ {{a}^{3}}/{{b}^{3}} \right]}^{x+y+z}}\]
B) \[{{\left[ {{a}^{2}}/{{b}^{2}} \right]}^{x+y+z}}\]
C) \[{{\left[ a/b \right]}^{\left( x+y+z \right)/2}}\]
D) \[{{\left[ a/b \right]}^{3\left( x+y+z \right)/2}}\]
Correct Answer: D
Solution :
(d): \[{{\left( \frac{a}{b} \right)}^{x+y+z}}\div \left[ {{\left( \frac{a}{b} \right)}^{\frac{-x}{2}}}\times {{\left( \frac{a}{b} \right)}^{\frac{-y}{2}}}\times {{\left( \frac{a}{b} \right)}^{\frac{-z}{2}}} \right]\] \[={{\left( \frac{a}{b} \right)}^{x+y+z}}\div \left[ {{\left( \frac{a}{b} \right)}^{\frac{-x-y-z}{2}}} \right]\] \[={{\left( \frac{a}{b} \right)}^{\left\{ x+y+z-\left( \frac{-x-y-z}{2} \right) \right\}}}\] \[={{\left( \frac{a}{b} \right)}^{\left\{ \frac{3}{2}x+y+z \right\}}}\].
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