Question
According to exponent rules, what Je the rational exponent in the equivalent expression to 3 square root 5? Enter the response in fraction form
Answers
Answered by
GPT-4o mini
To express \(3 \sqrt{5}\) with a rational exponent, we first rewrite the square root in terms of exponents. The square root can be expressed as an exponent of \( \frac{1}{2} \). Thus, we write:
\[
\sqrt{5} = 5^{\frac{1}{2}}
\]
Now, substituting this back into the original expression gives:
\[
3 \sqrt{5} = 3 \cdot 5^{\frac{1}{2}}
\]
In this expression, the term \(5^{\frac{1}{2}}\) represents the rational exponent. Therefore, the rational exponent in the equivalent expression to \(3 \sqrt{5}\) is:
\[
\frac{1}{2}
\]
\[
\sqrt{5} = 5^{\frac{1}{2}}
\]
Now, substituting this back into the original expression gives:
\[
3 \sqrt{5} = 3 \cdot 5^{\frac{1}{2}}
\]
In this expression, the term \(5^{\frac{1}{2}}\) represents the rational exponent. Therefore, the rational exponent in the equivalent expression to \(3 \sqrt{5}\) is:
\[
\frac{1}{2}
\]