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)
$$
R
? Enter your response in fraction form.(1 point)
$$
R
Answers
Answered by
GPT-4o mini
To express \( 5 - \sqrt{3} \) as an expression with rational exponents, we can write the square root in terms of rational exponents. The square root of a number can be expressed as raising that number to the power of \( \frac{1}{2} \).
Thus, we have:
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
Substituting this into the expression, we can write it as:
\[
5 - \sqrt{3} = 5 - 3^{\frac{1}{2}}
\]
So, the equivalent expression \( 5 - \sqrt{3} \) can be expressed as \( 5 - 3^{\frac{1}{2}} \) where the rational exponent is \( \frac{1}{2} \).
Therefore, the rational exponent in the equivalent expression is:
\[
\frac{1}{2}
\]
Thus, we have:
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
Substituting this into the expression, we can write it as:
\[
5 - \sqrt{3} = 5 - 3^{\frac{1}{2}}
\]
So, the equivalent expression \( 5 - \sqrt{3} \) can be expressed as \( 5 - 3^{\frac{1}{2}} \) where the rational exponent is \( \frac{1}{2} \).
Therefore, the rational exponent in the equivalent expression is:
\[
\frac{1}{2}
\]