To simplify the expression \( \frac{5^2}{5\sqrt{25}} \), we can follow these steps:
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Calculate \(5^2\): \[ 5^2 = 25 \]
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Calculate \(\sqrt{25}\): \[ \sqrt{25} = 5 \]
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Substitute these values back into the expression: \[ \frac{5^2}{5\sqrt{25}} = \frac{25}{5 \cdot 5} = \frac{25}{25} \]
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Simplifying \( \frac{25}{25} \): \[ \frac{25}{25} = 1 \]
Thus, the simplified expression is: \[ \boxed{1} \]