Given \(4725 = 3^a 5^b 7^c\), find:
(i) \(a, b, c\)
(ii) \(2^{-a} 3^b 7^c\)
Solution
\[ 4725 = 3^3 \times 5^2 \times 7^1 \]
\[ \Rightarrow a = 3,\quad b = 2,\quad c = 1 \]
(ii) Evaluate
\[ 2^{-a} 3^b 7^c = 2^{-3} \cdot 3^2 \cdot 7 \]
\[ = \frac{1}{8} \cdot 9 \cdot 7 \]
\[ = \frac{63}{8} \]
Final Answer:
\[ \boxed{a=3,\; b=2,\; c=1,\quad \frac{63}{8}} \]