Question

Given that the meaning of a rational exponent can be connected to the meaning of a root, how can you rewrite 5–√3 using a rational exponent?(1 point)
Responses

5^1
5 superscript 1 baseline

3^5
3 superscript 5 baseline

5^3
5 cubed

5 1/3

Answer 1

The expression \( 5 - \sqrt{3} \) does not relate directly to rewriting it using a rational exponent, as it involves subtraction rather than a single base raised to a power. However, if we focus solely on the square root portion \( \sqrt{3} \), it can be expressed using a rational exponent.

The square root of \( 3 \) can be rewritten as \( 3^{1/2} \).

If the context allows for focusing on the square root, the correct expression for \( \sqrt{3} \) using a rational exponent is:

\[
3^{1/2}
\]

But since the original expression was \( 5 - \sqrt{3} \), it remains \( 5 - 3^{1/2} \) if you rewrite the square root.

However, among the provided answers, if the goal is strictly to rewrite \( \sqrt{3} \) as a rational exponent, you would choose:

**None of the provided options accurately match \( 5 - \sqrt{3} \) as a whole.**

If we were to rewrite just \( \sqrt{3} \) though, the preferred representation is:

- \( 3^{1/2} \) (not given as an option).

Please select the most relevant choice based on what you are specifically asked to do. If the focus is solely on roots, consider discussing the representation \( 3^{1/2} \).