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Let a, b be any positive integers and x = 0 or 1, then
$$a^{x}b^{1-x}=xa+(1-x)b$$
$$a^{x}b^{1-x}=(1-x)a+xb$$
$$a^{x}b^{(1-x)}=a(1-x)bx$$
None of the above is necessarily true.
Putting value of x=0 or 1 and solving all four options, We will find that only option A satisfies the equation with both values, hence answer will be A.
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