Use the properties of operations and rules for multiplying and dividing to solve:

To solve the expression \((-3) \div (34) \times (27) \times (-516) \div (57)\), we can use the properties of operations. Here's a step-by-step breakdown:

1. **Rewrite the Expression**:
\[
(-3) \div 34 \times 27 \times (-516) \div 57
\]

2. **Group the Multiplications and Divisions**:
\[
= \left((-3) \div 34 \times (-516)\right) \div 57 \times 27
\]

3. **Handle Division First**:
Calculate \((-3) \div 34\):
\[
= -\frac{3}{34}
\]
Now we have:
\[
-\frac{3}{34} \times 27 \times (-516) \div 57
\]

4. **Calculate \(-3/34 \times 27\)**:
\[
-\frac{3 \times 27}{34} = -\frac{81}{34}
\]

5. **Next, Multiply by -516**:
\[
-\frac{81}{34} \times (-516) = \frac{81 \times 516}{34}
\]

6. **Calculate \(81 \times 516\)**:
\[
= 41796
\]
Now, we need to divide by \(34\):
\[
\frac{41796}{34}
\]

7. **Divide**:
\[
41796 \div 34 = 1235.176
\]

8. **Divide by 57**:
\[
\frac{1235.176}{57}
\]
\[
= 21.68
\]

Therefore, the final result of the expression \((-3) \div (34) \times (27) \times (-516) \div (57)\) is approximately **21.68**.