To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we focus on the term \( \sqrt{3} \) which can be expressed with a rational exponent.
The square root of a number can be expressed as raising that number to the power of \( \frac{1}{2} \). Hence, we can rewrite \( \sqrt{3} \) as:
\[ \sqrt{3} = 3^{\frac{1}{2}} \]
Therefore, \( 5 - \sqrt{3} \) can be seen as:
\[ 5 - 3^{\frac{1}{2}} \]
However, if you are asking to rewrite the term \( \sqrt{3} \) itself rather than \( 5 - \sqrt{3} \), then \( \sqrt{3} \) is equivalent to \( 3^{\frac{1}{2}} \).
If you meant to consider the options given in your responses and identify how to represent \( \sqrt{3} \) (not \( 5 - \sqrt{3} \)), the corresponding rational exponent representation among your responses would focus on \( \sqrt{3} \) and not directly ask for \( 5 - \sqrt{3} \).
Based on the context and options provided, you can write \( \sqrt{3} \) as \( 3^{\frac{1}{2}} \). If you are looking for an answer specifically for \( 5 - \sqrt{3} \), then it cannot be reduced further in terms of rational exponents as it is already in its simplest form.
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