The expression \( 5 - \sqrt{3} \) can be rewritten using a rational exponent for the square root. The square root of a number can be expressed with a rational exponent.
Specifically, the square root of 3 can be rewritten as \( 3^{1/2} \). Therefore, the expression \( \sqrt{3} \) is the same as \( 3^{1/2} \), and you could express it in another context if it was part of an exponentiation.
However, if you need to express just the square root in terms of a rational exponent, it would look like this:
\[ \sqrt{3} = 3^{1/2} \]
But if you were asked how to express \( 5 - \sqrt{3} \) using a rational exponent, it's a bit tricky since the expression involves subtraction.
From your options, it seems more relevant to focus on expressions related to rational exponents:
- \( 5^{3} \) is simply \( 5 \) cubed, but doesn't relate.
- \( 5^{1/3} \) is \( 5 \) raised to the one-third power.
- \( 5^{1} \) is simply \( 5 \).
- \( 3^{5} \) doesn't seem relevant either.
If the goal was specifically to focus on converting \( \sqrt{3} \), then while the answer options are a bit misleading, you would go with \( 3^{1/2} \) from an earlier context.
In summary, while \( 5 - \sqrt{3} \) doesn't plug directly into your options, the expression you need for \( \sqrt{3} \) is \( 3^{1/2} \). If you were meant to use just an exponent for \( 5 \) while discussing roots, there isn’t a direct connection aligning with the available options. You would want to clarify what the question specifically asked or your context about \( 5 - \sqrt{3} \) particularly in relation to rational exponents more.
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