How do you write an exponent as a fraction?

To write an exponent as a fraction, you can express it using a rational number in the form of a fraction. For example, if you have (x^{\frac{a}{b}}), it means you take the (b)-th root of (x) raised to the power of (a), or (\sqrt[b]{x^a}). This can also be represented as ((\sqrt[b]{x})^a). Thus, the exponent indicates both the root and the power applied to the base.