Given the operation defined by x∗y=xyx * y = x^yx∗y=xy,
x∗2=x ⟹ x2=xx * 2 = x \implies x^2 = xx∗2=x⟹x2=x
Rearranging gives: x2−x=0 ⟹ x(x−1)=0x^2 - x = 0 \implies x(x - 1) = 0x2−x=0⟹x(x−1)=0
Thus, the possible values of xxx are: 0 and 1\boxed{0 \text{ and } 1}0 and 1
