Proof by counter-example:
Let a = 3 and b = 1/2, therefore a^b is the square root of 3, which can’t be written as a ratio of two whole numbers, and is therefore irrational.
let a = 2 and b = 1/2
a^b = 2^(1/2) = sqrt(2) which is not a rational number
Therefore the statement is false
Let a=2, b=1/2, both rational.
a^b = 2^(1/2)= sqrt 2 which is irrational.
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