Question

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, you can focus on the square root part. The square root of a number can be expressed as a rational exponent of \( \frac{1}{2} \). Thus, \( \sqrt{3} \) can be rewritten as \( 3^{\frac{1}{2}} \).

However, your expression \( 5 - \sqrt{3} \) seems to suggest you're looking for the form of \( \sqrt{3} \) specifically under a rational exponent. Generally, the representation should be about the square root itself:

So,

\[ 5 - \sqrt{3} = 5 - 3^{\frac{1}{2}} \]

But since the question asks directly about \( \sqrt{3} \), it seems you're looking for the representation of \( \sqrt{3} \) alone in the options you've provided.

None of the provided options exactly match the expression \( 5 - \sqrt{3} \). However, if you're focusing solely on converting \( \sqrt{3} \) to a rational exponent, the option would be:

\( 3^{\frac{1}{2}} \)

But based on the specific choices you've provided in your question, it’s likely you needed a more specified transformation that directly references rational exponents without the negative context. If that is necessary, I would recommend verifying how the options relate to what you want to convert as \( 5 - \sqrt{3} \) wouldn’t directly be simplified further without additional context.