Given 4725 = 3a × 5b × 7c, find

Question:

Given $4725=3 \times 5 \times 7$, find

(i) The integral values of a, b and c

(ii) The value of $2^{-a} \times 3^{b} \times 7^{c}$

Solution:

(i) Taking out the LCM of 4725, we get

$3^{3} \times 5^{2} \times 7^{1}=3^{a} \times 5^{b} \times 7^{c}$

By comparing, we get

$a=3, b=2$ and $c=1$

(ii) The value of $2^{-a} \times 3^{b} \times 7^{c}$

Sol:

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

$2^{-3} \times 3^{2} \times 7^{1}=1 / 8 \times 9 \times 7$

$63 / 8$