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

5^3
5 cubed

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

3^5
3 superscript 5 baseline

5^1

Answer 1

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we first need to understand that the square root can be expressed as a fractional exponent. The square root of a number can be rewritten as raising that number to the power of \( \frac{1}{2} \).

Thus, we can rewrite \( \sqrt{3} \) as \( 3^{1/2} \). However, since the original expression is \( 5 - \sqrt{3} \), we focus only on rewriting \( \sqrt{3} \).

The expression \( 5 - \sqrt{3} \) doesn't lend itself to rewriting as a single term with a rational exponent. The options provided are more indicative of either a misunderstanding of what you are trying to achieve or a misinterpretation.

Therefore, from the options given, the correct way to express just the \( \sqrt{3} \) part in rational exponent form would be:

**5 - 3^{1/2}**

However, since that's not one of the answers provided, I cannot select from the options listed. If you specifically wanted to rewrite only \( \sqrt{3} \), the correct form of a root using a rational exponent on its own would be \( 3^{1/2} \), but since it's not an option we can select, we need clarification on the intent of the problem.