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Given $4725 = 3^a5^b7^c$, find the value of $2^{-a}3^b 7^c$.
Given:
$4725 = 3^a5^b7^c$
To do:
We have to find the value of $2^{-a}3^b 7^c$.
Solution:
Prime factorisation of 4725 is,
$4725=3^3\times5^2\times7^1$
Therefore,
$3^3\times5^2\times7^1=3^a \times 5^b \times 7^c$
Comparing both the sides, we get,
$a=3, b=2$ and $c=1$
This implies,$2^{-a}3^b 7^c=2^{-3}\times3^{2}\times7^{1}$
$=\frac{1}{8}\times9\times7$
$=\frac{63}{8}$
The value of $2^{-a}3^b 7^c$ is $\frac{63}{8}$.
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