Question:
If $1176=2 \times 3 \times 7$, find the values of $a, b$ and $c$.
Solution:
Hence compute the value of $2^{a} \times 3^{b} \times 7^{-c}$ as a fraction
$1176=2^{a} \times 3^{b} \times 7^{c}$
$2^{3} \times 3^{1} \times 7^{2}=2^{a} \times 3^{b} \times 7^{c}$
$a=3, b=1, c=2$
We have to find the value of $2^{a} \times 3^{b} \times 7^{-c}$
$2^{a} \times 3^{b} \times 7^{-c}=2^{3} \times 3^{1} \times 7^{-2}$
$=\frac{2 \times 2 \times 2 \times 3}{7 \times 7}$
$=24 / 49$
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