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 $c=1$

$2^{-a}3^b 7^c=2^{-3}\times3^{2}\times7^{1}$

$=\frac{1}{8}\times9\times7$

$=\frac{63}{8}$

The value of $2^{-a}3^b 7^c$ is $\frac{63}{8}$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

29 Views

Kickstart Your Career

Get certified by completing the course

Get Started