Question
Question
According to exponent rules, what is the rational exponent in the equivalent expression to 5–√3
? Enter your response in fraction form.(1 point)
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Answers
GPT-4o mini
To express the expression \( 5 - \sqrt{3} \) with a rational exponent, we first recognize that the square root can be rewritten using a rational exponent.
The square root of a number can be represented as that number raised to the power of \( \frac{1}{2} \). Therefore, we have:
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
Thus, the expression \( 5 - \sqrt{3} \) can be left as is because it is already in a simplified form, and we are looking for the rational exponent corresponding specifically to \( \sqrt{3} \).
The rational exponent for \( \sqrt{3} \) is \( \frac{1}{2} \).
Therefore, in fraction form, the rational exponent in the equivalent expression to \( \sqrt{3} \) is:
\[
\frac{1}{2}
\]
The square root of a number can be represented as that number raised to the power of \( \frac{1}{2} \). Therefore, we have:
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
Thus, the expression \( 5 - \sqrt{3} \) can be left as is because it is already in a simplified form, and we are looking for the rational exponent corresponding specifically to \( \sqrt{3} \).
The rational exponent for \( \sqrt{3} \) is \( \frac{1}{2} \).
Therefore, in fraction form, the rational exponent in the equivalent expression to \( \sqrt{3} \) is:
\[
\frac{1}{2}
\]