The expression \(\sqrt[4]{23}\) can be rewritten using exponents. The fourth root of a number can be expressed as that number raised to the power of \( \frac{1}{4} \). Therefore, we can rewrite \(\sqrt[4]{23}\) as:
\[ 23^{\frac{1}{4}} \]
So, the rational number that could be used as an exponent to rewrite \(\sqrt[4]{23}\) is \(\frac{1}{4}\).