A) \[-\frac{4}{9}{{x}^{4}}{{y}^{4}}{{z}^{4}}\]
B) \[\frac{4}{9}{{x}^{4}}{{y}^{4}}{{z}^{4}}\]
C) \[-\frac{4}{9}{{x}^{3}}{{y}^{3}}{{z}^{3}}\]
D) \[\frac{4}{9}{{x}^{3}}{{y}^{3}}{{z}^{3}}\]
Correct Answer: A
Solution :
We have \[\left( -5{{x}^{2}}y \right)\times \left( \frac{-2}{3}x{{y}^{2}}z \right)\times \left( \frac{8}{15}xy{{z}^{2}} \right)\times \left( \frac{-1}{4}z \right)\] \[=\left( -5\times \left( \frac{-2}{3} \right)\times \frac{8}{15}\times \left( \frac{-1}{4} \right) \right)\times \left( {{x}^{2}}\times x\times x \right)\] \[\times (y\times {{y}^{2}}\times y)\times (z\times {{z}^{2}}\times z)\] \[=\frac{-4}{9}{{x}^{4}}{{y}^{4}}{{z}^{4}}\]
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