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
5^1/3
5 superscript Start Fraction 1 over 3 End Fraction baseline
5^3
5 cubed
3^5
3 superscript 5 baseline
Responses
5^1
5 superscript 1 baseline
5^1/3
5 superscript Start Fraction 1 over 3 End Fraction baseline
5^3
5 cubed
3^5
3 superscript 5 baseline
Answers
GPT-4o mini
To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we need to focus on the term \( \sqrt{3} \). The square root of 3 can be expressed as a rational exponent:
\[
\sqrt{3} = 3^{1/2}
\]
So, \( 5 - \sqrt{3} \) can be rewritten as:
\[
5 - 3^{1/2}
\]
However, the original expression \( 5 - \sqrt{3} \) is not one of the choices provided. Among the options provided, the best choice that connects with the concept of rational exponents is:
\[
5^{1/3}
\]
This choice is not directly related to the original expression, but if you want to express \( \sqrt{3} \) itself, it would be equal to \( 3^{1/2} \), if those were options.
Given the choices you provided, technically we wouldn't transform \( 5 - \sqrt{3} \) into one of the answers since none are equivalent to the expression in question. Is there anything else you would like help with?
\[
\sqrt{3} = 3^{1/2}
\]
So, \( 5 - \sqrt{3} \) can be rewritten as:
\[
5 - 3^{1/2}
\]
However, the original expression \( 5 - \sqrt{3} \) is not one of the choices provided. Among the options provided, the best choice that connects with the concept of rational exponents is:
\[
5^{1/3}
\]
This choice is not directly related to the original expression, but if you want to express \( \sqrt{3} \) itself, it would be equal to \( 3^{1/2} \), if those were options.
Given the choices you provided, technically we wouldn't transform \( 5 - \sqrt{3} \) into one of the answers since none are equivalent to the expression in question. Is there anything else you would like help with?