Question 1199524
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256 = {{{2^8}}} = {{{4^4}}}.


The solutions to the problem are


        (1)  the pair  (a,b) = (2,4),

    and

        (2)  the pair  (a,b) = (4,1).


There is no other solutions in positive integer numbers.


<U>ANSWER</U>.  There are two different ordered pairs (a,b) that provide the solutions to the given equation.
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