The text appears to present a mathematical problem in Persian, and based on the format, it seems to involve absolute values and expressions involving $a, b, c$, where $a, b, c \in \mathbb{R}$ (real numbers) and $b, c > 0$. Let me interpret and solve the expressions systematically:

Problem Overview

The goal is to compute the following expressions under the given conditions:

1. $|ab|$
2. $|bc|$
3. $|c|$
4. $\left| \frac{ab}{c} \right|$

Solutions

1. $|ab|$:

The absolute value of a product is the product of the absolute values: $|ab| = |a| \cdot |b|$

2. $|bc|$:

Similarly, for $|bc|$: $|bc| = |b| \cdot |c|$

3. $|c|$:

This is already in simplified form: $|c| = |c|$

4. $\left| \frac{ab}{c} \right|$:

For the absolute value of a fraction: $\left| \frac{ab}{c} \right| = \frac{|ab|}{|c|}$ Substitute $|ab| = |a| \cdot |b|$: $\left| \frac{ab}{c} \right| = \frac{|a| \cdot |b|}{|c|}$

These solutions are general, as no specific values for $a, b, c$ are provided.

Would you like detailed examples with numerical values, or do you have further questions?

Follow-Up Questions:

1. How are absolute values defined for negative inputs, and why do they simplify as shown above?
2. What happens if $b$ or $c$ equals zero? Why is this case excluded here?
3. Can you calculate these values if specific values for $a, b, c$ are provided?
4. Why does the formula for the absolute value of a fraction work universally?
5. What practical applications involve such absolute value computations?

Tip: Always simplify expressions systematically, and remember that absolute values ensure all results are non-negative!