The equation shown in the image is:

$6^2 - (5 - 4) + 2(8 - 2^2) \div 8$

Let’s solve it step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Parentheses and Exponents

• First, solve any operations inside parentheses:
  • $5 - 4 = 1$
  • $2^2 = 4$, so $8 - 4 = 4$

The equation becomes: $6^2 - 1 + 2(4) \div 8$

Step 2: Exponents

• Now, evaluate the exponent $6^2 = 36$.

The equation is now: $36 - 1 + 2(4) \div 8$

Step 3: Multiplication and Division (left to right)

• Multiply $2(4) = 8$.
• Now, divide $8 \div 8 = 1$.

The equation simplifies to: $36 - 1 + 1$

Step 4: Addition and Subtraction (left to right)

• Subtract: $36 - 1 = 35$.
• Then add: $35 + 1 = 36$.

Final Answer:

$36$

Would you like a detailed explanation of any part of the process, or do you have any questions?

Here are five related questions you might find interesting:

1. How does the order of operations (PEMDAS) affect more complex equations?
2. How can we simplify complex expressions with multiple parentheses and exponents?
3. What is the importance of solving exponents before multiplication and division?
4. How would this equation change if the division came before multiplication in PEMDAS?
5. How can we check our work after solving multi-step problems like this?

Tip: Always solve inside parentheses first, and don’t forget to follow the order of operations strictly to avoid mistakes!