A) 1
B) \[{{a}^{P}}{{b}^{q}}{{c}^{r}}\]
C) \[{{a}^{q}}{{b}^{r}}{{c}^{p}}\]
D) \[{{a}^{r}}{{b}^{p}}{{c}^{q}}\]
Correct Answer: A
Solution :
\[a=A{{R}^{p-1}},\ b=A{{R}^{q-1}},\ c=A{{R}^{r-1}}\] \[\therefore \]\[{{\left( \frac{c}{b} \right)}^{p}}{{\left( \frac{b}{a} \right)}^{r}}{{\left( \frac{a}{c} \right)}^{q}}={{\left( \frac{A{{R}^{r-1}}}{A{{R}^{q-1}}} \right)}^{p}}{{\left( \frac{A{{R}^{q-1}}}{A{{R}^{p-1}}} \right)}^{r}}{{\left( \frac{A{{R}^{p-1}}}{A{{R}^{r-1}}} \right)}^{q}}\] \[={{R}^{(r-q)p+(q-p)r+(p-r)q}}={{R}^{0}}=1\].
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