https://file.aiquickdraw.com/mathbot/file/1727037305325qv17cpju.jpg

Simplify the expression. Write the answer in exponential notation

The expression in the image is:

\[
\frac{\left( \frac{3}{5} \cdot \frac{3}{5} \right)^3}{\left( \frac{3}{5} \right)^2}
\]

### Step-by-Step Simplification:

1. **Multiplying fractions in the numerator**:
   \[
   \frac{3}{5} \cdot \frac{3}{5} = \frac{9}{25}
   \]
   Now the expression becomes:
   \[
   \frac{\left( \frac{9}{25} \right)^3}{\left( \frac{3}{5} \right)^2}
   \]

2. **Simplifying the powers**:
   - Apply the exponent \(3\) to \(\frac{9}{25}\):
   \[
   \left( \frac{9}{25} \right)^3 = \frac{9^3}{25^3} = \frac{729}{15625}
   \]
   - Apply the exponent \(2\) to \(\frac{3}{5}\):
   \[
   \left( \frac{3}{5} \right)^2 = \frac{9}{25}
   \]
   Now the expression is:
   \[
   \frac{\frac{729}{15625}}{\frac{9}{25}}
   \]

3. **Dividing the fractions**:
   When dividing fractions, multiply the first fraction by the reciprocal of the second:
   \[
   \frac{729}{15625} \cdot \frac{25}{9} = \frac{729 \cdot 25}{15625 \cdot 9}
   \]

4. **Simplifying the multiplication**:
   \[
   \frac{729 \cdot 25}{15625 \cdot 9} = \frac{18225}{140625}
   \]
   Divide both the numerator and denominator by 2025 (which is their GCD):
   \[
   \frac{18225 \div 2025}{140625 \div 2025} = \frac{9}{69}
   \]
   Finally, divide again by 3:
   \[
   \frac{9 \div 3}{69 \div 3} = \frac{3}{23}
   \]

Thus, the simplified answer in its final form is:

\[
\boxed{\frac{3}{23}}
\]

Let me know if you'd like more details or further clarification on any step.

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### Related questions:
1. How do you simplify expressions with exponents and fractions?
2. What are the rules for multiplying and dividing fractions with exponents?
3. What is the general method for simplifying fractional exponents?
4. How can you find the greatest common divisor (GCD) of large numbers?
5. Why is it important to simplify expressions in exponential form?

**Tip**: When dividing fractions, remember that you multiply by the reciprocal of the divisor. This often helps simplify complex expressions quickly.

Simplify the expression. Write the answer in exponential notation.

Learn how to simplify an expression involving fractions raised to exponents. This problem applies the power of a power rule and involves fraction multiplication and division. Suitable for students in Grades 9-11.

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