Assuming that this question is asking why some number in radical form can be expressed in exponential form of rational number. And also assuming "rational" indicates a fraction form.
A rational number is real, and can be written in fraction form as a ratio. And if the number given is negative, the result can be the product of real number in exponential form and "i", imaginary number.
Thus, the answe is: Becase the number given with root sign is rational and positive.
The following are a few examples:
√0.4444...=√(4/9)=(4/9)^½
∜0.296296296...=∜(8/27)=(8/27)^¼
√1.4=√(7/5)=(7/5)^½