Let's analyze the mathematical expression in the image:

The expression is:

$\frac{-12(-5 - 3)^2}{-6}$

Step-by-Step Solution:

1. Simplify the parentheses: Inside the parentheses, calculate $(-5 - 3)$: $-5 - 3 = -8$ So the expression becomes: $\frac{-12(-8)^2}{-6}$

2. Square the value inside the parentheses: $(-8)^2 = 64$. Now, the expression becomes: $\frac{-12(64)}{-6}$

3. Multiply: Multiply $-12$ by $64$: $-12 \times 64 = -768$ So the expression becomes: $\frac{-768}{-6}$

4. Simplify the division: Divide $-768$ by $-6$: $\frac{-768}{-6} = 128$

Final Answer:

The value of the expression is: $\boxed{128}$

Would you like more details or have any questions?

Related Questions:

1. What happens if the division involves decimals instead of integers?
2. How does squaring a negative number always yield a positive result?
3. Can this expression be simplified further if the numerator or denominator is more complex?
4. How would the result change if the numerator or denominator were positive instead?
5. Why does dividing two negatives result in a positive number?

Tip:

Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to ensure correct calculations!