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According to exponent rules, what is the rational exponent in the equivalent expression to 5–√3 ? Enter your response in fracti...Question
According to exponent rules, what is the rational exponent in the equivalent expression to 5–√3
? Enter your response in fraction form.
? Enter your response in fraction form.
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what is 3√5's rational exponent
Answered by
GPT-4o mini
The expression \( 5 - \sqrt{3} \) can be rewritten in terms of rational exponents. The square root can be expressed as a fractional exponent. Specifically, the square root of 3, \( \sqrt{3} \), can be expressed as \( 3^{1/2} \).
Thus, we can rewrite the expression:
\[
5 - \sqrt{3} = 5 - 3^{1/2}
\]
Here, the rational exponent for \( \sqrt{3} \) is \( \frac{1}{2} \).
If you meant to find the rational exponent of the entire expression \( 5 - \sqrt{3} \) relative to a specific operation (like raising it to a power or manipulating it further), please clarify that. However, in its current context, the rational exponent related to the square root is \( \frac{1}{2} \).
Thus, we can rewrite the expression:
\[
5 - \sqrt{3} = 5 - 3^{1/2}
\]
Here, the rational exponent for \( \sqrt{3} \) is \( \frac{1}{2} \).
If you meant to find the rational exponent of the entire expression \( 5 - \sqrt{3} \) relative to a specific operation (like raising it to a power or manipulating it further), please clarify that. However, in its current context, the rational exponent related to the square root is \( \frac{1}{2} \).
Answered by
GPT-4o mini
Apologies for the misunderstanding.
If you are asking for the rational exponent of the expression \( 5 - \sqrt{3} \) as a whole (rather than focusing on the \(\sqrt{3}\) part), it seems like we need to clarify what you mean by "rational exponent". The expression itself does not have a straightforward rational exponent unless it is part of a larger expression or term.
If you are asking specifically about the square root component, the square root \(\sqrt{3}\) would indeed have a rational exponent of \( \frac{1}{2} \), suggesting that you're interested in that part.
However, if the question involves a misunderstanding or an error in interpreting what you mean by the rational exponent for the entire expression \( 5 - \sqrt{3} \), I could guide you in the right way if you provide additional context or clarification.
If you'd like a different aspect explored, please let me know!
If you are asking for the rational exponent of the expression \( 5 - \sqrt{3} \) as a whole (rather than focusing on the \(\sqrt{3}\) part), it seems like we need to clarify what you mean by "rational exponent". The expression itself does not have a straightforward rational exponent unless it is part of a larger expression or term.
If you are asking specifically about the square root component, the square root \(\sqrt{3}\) would indeed have a rational exponent of \( \frac{1}{2} \), suggesting that you're interested in that part.
However, if the question involves a misunderstanding or an error in interpreting what you mean by the rational exponent for the entire expression \( 5 - \sqrt{3} \), I could guide you in the right way if you provide additional context or clarification.
If you'd like a different aspect explored, please let me know!
Answered by
GPT-4o mini
To express the cube root of 5, denoted as \( \sqrt[3]{5} \), in terms of rational exponents, you use the following conversion:
\[
\sqrt[3]{5} = 5^{1/3}
\]
So, the rational exponent for \( \sqrt[3]{5} \) is \( \frac{1}{3} \).
\[
\sqrt[3]{5} = 5^{1/3}
\]
So, the rational exponent for \( \sqrt[3]{5} \) is \( \frac{1}{3} \).