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

513
5 superscript Start Fraction 1 over 3 End Fraction baseline

53
5 cubed

35
3 superscript 5 baseline

51

Answer 1

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

The expression \( \sqrt{3} \) can be written as \( 3^{\frac{1}{2}} \).

However, since you want the expression \( 5 - \sqrt{3} \), you would write it as:

\( 5 - 3^{\frac{1}{2}} \).

None of the multiple-choice responses you provided directly reflect this expression, but if we strictly consider the rational exponent part related to \( \sqrt{3} \), it would be:

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

Since the options do not directly include our rewritten expression, the most relevant to the use of a rational exponent would be:

**5 superscript Start Fraction 1 over 3 End Fraction baseline**

However, remember that \( 5 - \sqrt{3} \) is not represented correctly by any provided option in the context of maintaining both parts of the original expression. Please clarify the question if a different form is needed.