https://file.aiquickdraw.com/mathbot/file/1722746503437ycof352r.jpg

The given expression is:

\[
\left(\frac{\frac{a}{b}}{c}\right) \cdot \frac{a}{\left(\frac{b}{c}\right)}
\]

Let's simplify this step by step.

1. **Simplify the first fraction:**

   \[
   \frac{\frac{a}{b}}{c} = \frac{a}{bc}
   \]

2. **Simplify the second fraction:**

   \[
   \frac{a}{\left(\frac{b}{c}\right)} = \frac{a}{b/c} = \frac{a \cdot c}{b}
   \]

3. **Multiply the simplified fractions:**

   \[
   \frac{a}{bc} \cdot \frac{ac}{b} = \frac{a \cdot a \cdot c}{b \cdot b \cdot c} = \frac{a^2c}{b^2c}
   \]

4. **Further simplification:**

   \[
   \frac{a^2c}{b^2c} = \frac{a^2}{b^2}
   \]

So, the simplified expression is:

\[
\frac{a^2}{b^2}
\]

Would you like further details or have any questions?

### Related Questions:

1. How can we simplify complex fractions?
2. What are the properties of exponents used in simplification?
3. How do you multiply fractions?
4. Can we simplify the expression \(\frac{a^3}{b^3}\) similarly?
5. What is the general rule for dividing by a fraction?
6. How can the associative property of multiplication aid in simplification?
7. How does canceling common factors work in algebraic fractions?
8. What are the steps to simplify a nested fraction?

### Tip:
When simplifying fractions involving variables, always look for common factors in the numerator and the denominator that can be canceled out. This can significantly simplify the expression.

Learn how to simplify the fraction (a/b)/c * a/(b/c) step-by-step with a detailed solution. This problem involves key algebraic concepts such as fraction simplification and is suitable for students in Grades 7-9.

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