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.