If $1176=2a×3b×7c,find the values of a,b and c. Hence,compute the value of 2a×3b×7−c as a fraction.$

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Solution

$1176 = 2^{a} \times 3^{b} \times 7^{c}$

$2^{a} \times 3^{b} \times 7^{c} = 2^{3} \times 3^{1} \times 7^{2} C o m p a r i n g, w e g e t a = 3, b = 1, c = 2 ∴ 2^{a} \times 3^{b} \times 7^{- c} = 2^{3} \times 3^{1} \times 7^{- 2} = 8 \times 3 \times \frac{1}{49} = \frac{24}{49}$

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