Question

Given $4725=3^a{5}^b{7}^c$, find
i) the integral values of a,b and c.
ii) the value of $2^{-a}{3}^b{7}^c$

Answer 1

i) Image

$\Rightarrow 4725=3^3\times 5^2\times 7^1$

$\Rightarrow a=3,b=2,c=1$

ii) $2^{-a}{3}^b{7}^c=2^{-3}\times 3^2\times 7^1$

$=\frac{9\times 7}{8}=\frac{63}{8}$