Let's solve the problem step by step using the order of operations (PEMDAS/BODMAS):

The given expression:

$9 \times (10 \div 5)^2 \div 3$

Step 1: Simplify inside the parentheses.

$10 \div 5 = 2$

So, the expression becomes: $9 \times (2)^2 \div 3$

Step 2: Evaluate the exponent.

$2^2 = 4$

Now, the expression is: $9 \times 4 \div 3$

Step 3: Perform multiplication and division from left to right.

1. First, multiply: $9 \times 4 = 36$

2. Then, divide: $36 \div 3 = 12$

Final Answer:

The simplified expression equals 12.

Would you like further details or explanation? Here are five related questions to consider:

1. How does the order of operations (PEMDAS) work, and why is it important?
2. What happens if we change the parentheses in an expression like this?
3. How can we evaluate more complex expressions involving exponents and roots?
4. Why do we perform division and multiplication from left to right?
5. Can you simplify an expression with nested parentheses and multiple exponents?

Tip:

Always simplify parentheses first and carefully follow the order of operations to avoid mistakes!