Question
What rational number could be used as an exponent to rewrite 20−−√5205?(1 point) The rational number that could be used as an exponent is .
Answers
GPT-4o mini
To rewrite the expression \( \frac{\sqrt{20}}{5205} \) using a rational number as an exponent, we first need to simplify the expression.
1. Rewrite the square root in exponential form:
\( \sqrt{20} = 20^{1/2} \).
2. Now, we can write the expression as:
\[
\frac{20^{1/2}}{5205}.
\]
If you are looking for a specific rational exponent to express \( \frac{\sqrt{20}}{5205} \), you could express it in a form that combines these two terms.
However, we could also consider \( 5205 \) as \( 5205^{1} \), so we could write:
\[
\frac{20^{1/2}}{5205} = 20^{1/2} \cdot 5205^{-1}.
\]
Thus, the rational exponent that could be used as an exponent is \( \frac{1}{2} \) for the \( 20 \) and \( -1 \) for the \( 5205 \).
Therefore, the rational number that could be used as an exponent is \( \frac{1}{2} \) (for \( 20 \)). If the context requires both terms be handled together somehow, please let me know.
1. Rewrite the square root in exponential form:
\( \sqrt{20} = 20^{1/2} \).
2. Now, we can write the expression as:
\[
\frac{20^{1/2}}{5205}.
\]
If you are looking for a specific rational exponent to express \( \frac{\sqrt{20}}{5205} \), you could express it in a form that combines these two terms.
However, we could also consider \( 5205 \) as \( 5205^{1} \), so we could write:
\[
\frac{20^{1/2}}{5205} = 20^{1/2} \cdot 5205^{-1}.
\]
Thus, the rational exponent that could be used as an exponent is \( \frac{1}{2} \) for the \( 20 \) and \( -1 \) for the \( 5205 \).
Therefore, the rational number that could be used as an exponent is \( \frac{1}{2} \) (for \( 20 \)). If the context requires both terms be handled together somehow, please let me know.