Mark the correct alternative in the following question:

$If x y z = 0, then find the value of {(a^{x})}^{y z} + {(a^{y})}^{z x} + {(a^{z})}^{x y} = (a) 3 (b) 2 (c) 1 (d) 0$

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Solution

Since,

${(a^{x})}^{y z} + {(a^{y})}^{z x} + {(a^{z})}^{x y} = a^{x y z} + a^{y z x} + a^{z x y} [As, {(x^{m})}^{n} = x^{m n}] = a^{x y z} + a^{x y z} + a^{x y z} = a^{0} + a^{0} + a^{0} = 1 + 1 + 1 (As, x^{0} = 1) = 3$

Hence, the correct option is (a).

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