The expression you provided involves division by zero, which is undefined in mathematics. Let's break it down to identify where these undefined operations occur:

### Expression:
\[
\left(\frac{(1 \times 0)}{5} - \frac{2}{(3 \times 0)}\right)^3 \div \left(\frac{3}{(2 \times 0)} \times \frac{10}{9}\right)
\]

### Steps:

1. **First term inside the parentheses:**
   \[
   \frac{1 \times 0}{5} = \frac{0}{5} = 0
   \]
   
2. **Second term inside the parentheses:**
   \[
   \frac{2}{3 \times 0} = \frac{2}{0}
   \]
   Division by zero here makes the expression undefined.

3. **Expression inside the parentheses:**
   \[
   0 - \frac{2}{0}
   \]
   Since \(\frac{2}{0}\) is undefined, the entire expression inside the parentheses becomes undefined.

4. **The entire expression:**
   \[
   \text{Undefined}^3 \div \left(\frac{3}{2 \times 0} \times \frac{10}{9}\right)
   \]
   The undefined value propagates through the entire expression, making the overall expression undefined.

### Conclusion:
This expression is **undefined** because it involves division by zero multiple times.

Would you like more details or have any questions?

### Related Questions:
1. What is division by zero and why is it undefined?
2. How can undefined operations affect the outcome of complex mathematical expressions?
3. What are some common scenarios where division by zero might occur unintentionally?
4. Can you provide examples of how to simplify expressions before encountering division by zero?
5. How is division by zero treated in different branches of mathematics?

**Tip:** Always check for potential division by zero early in the problem-solving process to avoid undefined expressions.

Explore the concept of division by zero in mathematical expressions with a detailed breakdown of the problem ((1*0)/5-2/(3*0))^3/(3/(2*0)*10/9). Understand why this expression is undefined and the implications of division by zero in mathematical calculations.

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