If the sum of a,b,c is an even prime number, then find the value of $2^{4 a - b - c} \times 2^{4 b - c - a} \times 2^{4 c - a - b} \times 2^{4 c - a - b}$

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Solution

Only even prime is 2. $\Rightarrow a + b + c = 2$
$∴ 2^{4 a - b - c} {.2}^{4 b - c - a} {.2}^{4 c - a - b}$
$= 2^{4 a - 2 a + 4 b - 2 b + 4 c - 2 c}$ (using the property $a^{m} . a^{n} = a^{m + n})$
$= 2^{2 a + 2 b + 2 c} = 2^{2 (a + b + c)} = 2^{2 (2)} = 2^{4} = 16$

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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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