Let’s evaluate the given expression step by step:

Expression:

$10 - 8 \left[ (7 + 4) - 6 \left\{ (7 - 3)^2 - (9 - 7)^3 \right\} \right]$

Step 1: Simplify the innermost brackets

• $(7 - 3)^2 = 4^2 = 16$
• $(9 - 7)^3 = 2^3 = 8$

So the inner curly bracket becomes: $16 - 8 = 8$

Step 2: Replace and simplify the curly brackets

The expression now becomes: $10 - 8 \left[ (7 + 4) - 6(8) \right]$

Step 3: Simplify the square brackets

• $7 + 4 = 11$
• $6 \cdot 8 = 48$
• $11 - 48 = -37$

The expression is now: $10 - 8(-37)$

Step 4: Simplify the remaining operations

• $8 \cdot (-37) = -296$
• $10 - (-296) = 10 + 296 = 306$

Final Answer:

$\boxed{306}$

Would you like me to explain any specific step in more detail or help with similar problems?

Related Questions:

1. How would this problem change if exponents were higher, e.g., $(7-3)^3$ or $(9-7)^4$?
2. Can we generalize the process for solving nested brackets like these?
3. What happens if negative numbers are involved in the powers?
4. How would this calculation be implemented using a programming language or calculator?
5. How can we verify the result step by step using estimation?

Tip:

Always resolve the innermost brackets first in complex expressions to avoid mistakes!