To simplify the expression \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) using the quotient property, we first need to convert the mixed numbers into improper fractions.
- Convert \( 9 \frac{3}{5} \):
\[ 9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{9 \cdot 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5} \]
- Convert \( 9 \frac{1}{5} \):
\[ 9 \frac{1}{5} = 9 + \frac{1}{5} = \frac{9 \cdot 5 + 1}{5} = \frac{45 + 1}{5} = \frac{46}{5} \]
Now, we can rewrite the original expression using these improper fractions:
\[ \frac{9 \frac{3}{5}}{9 \frac{1}{5}} = \frac{\frac{48}{5}}{\frac{46}{5}} \]
- Use the property of division of fractions:
\[ \frac{\frac{48}{5}}{\frac{46}{5}} = \frac{48}{5} \times \frac{5}{46} = \frac{48 \cdot 5}{5 \cdot 46} \]
The \( 5 \) cancels out:
\[ = \frac{48}{46} \]
- Simplify \( \frac{48}{46} \):
\[ = \frac{24}{23} \]
So, the expression \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) simplifies to \( \frac{24}{23} \).
Final Answer
The simplified result of \( \frac{9 \frac{3}{5}}{9 \frac{1}{5}} \) is \( \frac{24}{23} \), and if you're asking for a specific exponent to be handled, please clarify the context for "9 □." However, based on the exponents of 9, this simplification does not directly involve exponents to define. If looking for a number in powers of 9, you could relate it by expressing if needed as \( 9^{(some exponent)} \), but generally, the fraction reduces to \( \frac{24}{23} \).