To rewrite the expression \( \frac{\sqrt{20}}{5205} \) using a rational number as an exponent, we first need to simplify the expression.
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Rewrite the square root in exponential form: \( \sqrt{20} = 20^{1/2} \).
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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.
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