If the sum of $a$ , $b$ and $c$ is equal to the even prime, then find the value of $2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b}$ .

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Solution

The only even prime is $2$ .

$a + b + c = 2$ ................. (1)

$2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b} = 2^{4 a - b - c + 4 b - c - a + 4 c - a - b}$

$2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b} = 2^{2 a + 2 b + 2 c}$

$2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b} = 2^{2 (a + b + c)}$ ................. (2)

Substitute $(1)$ in $(2)$

$2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b} = 2^{2 (2)}$

= $2^{4}$

= $16$ .

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