According to exponent rules, what is the rational exponent in the equivalent expression to 5–√3

Question

? Enter your response in fraction form.

Answer 1

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 \( \frac{1}{2} \).

Answer 2

wrong

Answer 3

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!

Answer 4

what is 3√5's rational exponent

Answer 5

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 \( \frac{1}{3} \).