To use the quotient property for the expression \( 9 \frac{3}{5} \div 9 \frac{1}{5} \), we first convert the mixed numbers into improper fractions.
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Convert the mixed numbers:
- \( 9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{45}{5} + \frac{3}{5} = \frac{48}{5} \)
- \( 9 \frac{1}{5} = 9 + \frac{1}{5} = \frac{45}{5} + \frac{1}{5} = \frac{46}{5} \)
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Set up the division of the improper fractions: \[ \frac{48}{5} \div \frac{46}{5} \]
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Use the property of division (multiplying by the reciprocal): \[ \frac{48}{5} \times \frac{5}{46} = \frac{48 \times 5}{5 \times 46} = \frac{48}{46} \]
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Simplify the fraction: \[ \frac{48}{46} = \frac{24}{23} \]
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Convert back to a mixed number if necessary:
- Since \( 24 < 23 \) is not the case, we keep it in the improper fraction form.
Since the question refers to a "simplified exponent" and uses the quotient property, we might also need to interpret the division in terms of powers. This would suggest evaluating the expression in terms of exponents, but in the context of the numbers, we didn't have any base numbers with exponents.
However, if we symbolize \( 9 \frac{3}{5} \) and \( 9 \frac{1}{5} \) each as powers of the number \( 9 \):
- \( 9^{3/5} \) and \( 9^{1/5} \) can be used due to the resemblance of \( 9 \div 9 \).
Thus, applying the quotient property \( a^m \div a^n = a^{m-n} \):
\[ 9^{\frac{3}{5} - \frac{1}{5}} = 9^{\frac{2}{5}}. \]
Therefore, the resultant expression simplifies to: \[ 9^{\frac{2}{5}}. \]
Thus, expressing it in the given format for the answer: Answer: \( 9^{\frac{2}{5}} \text{ leading to } 9□ , \text{ where } □ = \frac{2}{5}. \)
Hence the final answer is: 9□, with □ = 2/5.