Math worksheet practicing order of operations with detailed solutions.

The provided image is a worksheet titled "Order of Operations (A)" from Math-Drills.com. It involves solving mathematical expressions using the correct order of operations, which follows the PEMDAS/BODMAS rule:

PEMDAS/BODMAS Rule Recap:

1. Parentheses/Brackets (`()` or `[]`)
2. Exponents/Orders (Powers and Square Roots)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

---

Solutions to Each Expression:

#### Expression 1:
\[
(10 + 2) - 5 \times (6^2 \div (8 - 4))
\]

1. Solve inside parentheses:
\[
10 + 2 = 12 \quad \text{and} \quad 8 - 4 = 4
\]
So the expression becomes:
\[
12 - 5 \times (6^2 \div 4)
\]

2. Solve exponents:
\[
6^2 = 36
\]
So the expression becomes:
\[
12 - 5 \times (36 \div 4)
\]

3. Perform division inside parentheses:
\[
36 \div 4 = 9
\]
So the expression becomes:
\[
12 - 5 \times 9
\]

4. Perform multiplication:
\[
5 \times 9 = 45
\]
So the expression becomes:
\[
12 - 45
\]

5. Perform subtraction:
\[
12 - 45 = -33
\]

Final Answer:
\[
\boxed{-33}
\]

---

#### Expression 2:
\[
10 + 8 - 6^2 \div (9 \times 4)
\]

1. Solve exponents:
\[
6^2 = 36
\]
So the expression becomes:
\[
10 + 8 - 36 \div (9 \times 4)
\]

2. Solve multiplication inside parentheses:
\[
9 \times 4 = 36
\]
So the expression becomes:
\[
10 + 8 - 36 \div 36
\]

3. Perform division:
\[
36 \div 36 = 1
\]
So the expression becomes:
\[
10 + 8 - 1
\]

4. Perform addition and subtraction from left to right:
\[
10 + 8 = 18
\]
\[
18 - 1 = 17
\]

Final Answer:
\[
\boxed{17}
\]

---

#### Expression 3:
\[
8 \div (10 - 9)^2 \times 7 + 4^2
\]

1. Solve inside parentheses:
\[
10 - 9 = 1
\]
So the expression becomes:
\[
8 \div 1^2 \times 7 + 4^2
\]

2. Solve exponents:
\[
1^2 = 1 \quad \text{and} \quad 4^2 = 16
\]
So the expression becomes:
\[
8 \div 1 \times 7 + 16
\]

3. Perform division:
\[
8 \div 1 = 8
\]
So the expression becomes:
\[
8 \times 7 + 16
\]

4. Perform multiplication:
\[
8 \times 7 = 56
\]
So the expression becomes:
\[
56 + 16
\]

5. Perform addition:
\[
56 + 16 = 72
\]

Final Answer:
\[
\boxed{72}
\]

---

#### Expression 4:
\[
(10 \times (6 + 4)) \div (2^3 - 7)^2
\]

1. Solve inside parentheses:
\[
6 + 4 = 10 \quad \text{and} \quad 2^3 = 8
\]
So the expression becomes:
\[
(10 \times 10) \div (8 - 7)^2
\]

2. Perform subtraction inside parentheses:
\[
8 - 7 = 1
\]
So the expression becomes:
\[
(10 \times 10) \div 1^2
\]

3. Solve exponents:
\[
1^2 = 1
\]
So the expression becomes:
\[
(10 \times 10) \div 1
\]

4. Perform multiplication:
\[
10 \times 10 = 100
\]
So the expression becomes:
\[
100 \div 1
\]

5. Perform division:
\[
100 \div 1 = 100
\]

Final Answer:
\[
\boxed{100}
\]

---

#### Expression 5:
\[
(8 + 5^2) \times ((9 - 7)^2 \div 2)
\]

1. Solve exponents:
\[
5^2 = 25
\]
So the expression becomes:
\[
(8 + 25) \times ((9 - 7)^2 \div 2)
\]

2. Solve inside parentheses:
\[
8 + 25 = 33 \quad \text{and} \quad 9 - 7 = 2
\]
So the expression becomes:
\[
33 \times (2^2 \div 2)
\]

3. Solve exponents:
\[
2^2 = 4
\]
So the expression becomes:
\[
33 \times (4 \div 2)
\]

4. Perform division:
\[
4 \div 2 = 2
\]
So the expression becomes:
\[
33 \times 2
\]

5. Perform multiplication:
\[
33 \times 2 = 66
\]

Final Answer:
\[
\boxed{66}
\]

---

#### Expression 6:
\[
(3 + 9) \div 6 - 2 \times 8 \div 4^2
\]

1. Solve inside parentheses:
\[
3 + 9 = 12
\]
So the expression becomes:
\[
12 \div 6 - 2 \times 8 \div 4^2
\]

2. Solve exponents:
\[
4^2 = 16
\]
So the expression becomes:
\[
12 \div 6 - 2 \times 8 \div 16
\]

3. Perform division and multiplication from left to right:
\[
12 \div 6 = 2
\]
So the expression becomes:
\[
2 - 2 \times 8 \div 16
\]

Next, perform the multiplication:
\[
2 \times 8 = 16
\]
So the expression becomes:
\[
2 - 16 \div 16
\]

Finally, perform the division:
\[
16 \div 16 = 1
\]
So the expression becomes:
\[
2 - 1
\]

4. Perform subtraction:
\[
2 - 1 = 1
\]

Final Answer:
\[
\boxed{1}
\]

---

Summary of Final Answers:

1. \(\boxed{-33}\)
2. \(\boxed{17}\)
3. \(\boxed{72}\)
4. \(\boxed{100}\)
5. \(\boxed{66}\)
6. \(\boxed{1}\)