Math worksheet for practicing order of operations (PEMDAS) with eight problems.

To solve the given problems using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we will carefully evaluate each expression step by step.

---

Problem 1: \( 11^2 - [3 \times (8 - 5)^2] - 19 \)

1. Parentheses: Solve the innermost parentheses first.
\[
8 - 5 = 3
\]
So the expression becomes:
\[
11^2 - [3 \times 3^2] - 19
\]

2. Exponents: Evaluate the exponents.
\[
11^2 = 121 \quad \text{and} \quad 3^2 = 9
\]
So the expression becomes:
\[
121 - [3 \times 9] - 19
\]

3. Multiplication: Perform the multiplication inside the brackets.
\[
3 \times 9 = 27
\]
So the expression becomes:
\[
121 - 27 - 19
\]

4. Subtraction: Perform the subtraction from left to right.
\[
121 - 27 = 94
\]
\[
94 - 19 = 75
\]

Final Answer for Problem 1:
\[
\boxed{75}
\]

---

Problem 2: \( 6 \times 3 - (-9) + 7^2 \)

1. Exponents: Evaluate the exponent.
\[
7^2 = 49
\]
So the expression becomes:
\[
6 \times 3 - (-9) + 49
\]

2. Multiplication: Perform the multiplication.
\[
6 \times 3 = 18
\]
So the expression becomes:
\[
18 - (-9) + 49
\]

3. Subtraction and Addition: Simplify the subtraction of a negative number and then perform addition.
\[
18 - (-9) = 18 + 9 = 27
\]
\[
27 + 49 = 76
\]

Final Answer for Problem 2:
\[
\boxed{76}
\]

---

Problem 3: \( 6^2 - 3 \times (3^2 \times 2) + 4 \)

1. Exponents: Evaluate the exponents.
\[
6^2 = 36 \quad \text{and} \quad 3^2 = 9
\]
So the expression becomes:
\[
36 - 3 \times (9 \times 2) + 4
\]

2. Parentheses: Solve the multiplication inside the parentheses.
\[
9 \times 2 = 18
\]
So the expression becomes:
\[
36 - 3 \times 18 + 4
\]

3. Multiplication: Perform the multiplication.
\[
3 \times 18 = 54
\]
So the expression becomes:
\[
36 - 54 + 4
\]

4. Subtraction and Addition: Perform the subtraction and addition from left to right.
\[
36 - 54 = -18
\]
\[
-18 + 4 = -14
\]

Final Answer for Problem 3:
\[
\boxed{-14}
\]

---

Problem 4: \( (15 - 9)^2 \div (7 - 4)^2 \)

1. Parentheses: Solve the expressions inside the parentheses.
\[
15 - 9 = 6 \quad \text{and} \quad 7 - 4 = 3
\]
So the expression becomes:
\[
6^2 \div 3^2
\]

2. Exponents: Evaluate the exponents.
\[
6^2 = 36 \quad \text{and} \quad 3^2 = 9
\]
So the expression becomes:
\[
36 \div 9
\]

3. Division: Perform the division.
\[
36 \div 9 = 4
\]

Final Answer for Problem 4:
\[
\boxed{4}
\]

---

Problem 5: \( 4^3 \div 8 - [(6 + 18) \div 6] - 3 \)

1. Exponents: Evaluate the exponent.
\[
4^3 = 64
\]
So the expression becomes:
\[
64 \div 8 - [(6 + 18) \div 6] - 3
\]

2. Parentheses: Solve the expression inside the parentheses.
\[
6 + 18 = 24
\]
So the expression becomes:
\[
64 \div 8 - [24 \div 6] - 3
\]

3. Division: Perform the divisions.
\[
64 \div 8 = 8 \quad \text{and} \quad 24 \div 6 = 4
\]
So the expression becomes:
\[
8 - 4 - 3
\]

4. Subtraction: Perform the subtraction from left to right.
\[
8 - 4 = 4
\]
\[
4 - 3 = 1
\]

Final Answer for Problem 5:
\[
\boxed{1}
\]

---

Problem 6: \( (12^2 - 15 + 17) \times 16 \)

1. Exponents: Evaluate the exponent.
\[
12^2 = 144
\]
So the expression becomes:
\[
(144 - 15 + 17) \times 16
\]

2. Addition and Subtraction: Perform the operations inside the parentheses from left to right.
\[
144 - 15 = 129
\]
\[
129 + 17 = 146
\]
So the expression becomes:
\[
146 \times 16
\]

3. Multiplication: Perform the multiplication.
\[
146 \times 16 = 2336
\]

Final Answer for Problem 6:
\[
\boxed{2336}
\]

---

Problem 7: \( (13 + 8)^2 \div (14 - 11) \)

1. Parentheses: Solve the expressions inside the parentheses.
\[
13 + 8 = 21 \quad \text{and} \quad 14 - 11 = 3
\]
So the expression becomes:
\[
21^2 \div 3
\]

2. Exponents: Evaluate the exponent.
\[
21^2 = 441
\]
So the expression becomes:
\[
441 \div 3
\]

3. Division: Perform the division.
\[
441 \div 3 = 147
\]

Final Answer for Problem 7:
\[
\boxed{147}
\]

---

Problem 8: \( 4^2 + (20 - 14)^2 \div 2 \)

1. Exponents and Parentheses: Evaluate the exponents and the expression inside the parentheses.
\[
4^2 = 16 \quad \text{and} \quad 20 - 14 = 6
\]
So the expression becomes:
\[
16 + 6^2 \div 2
\]

2. Exponents: Evaluate the remaining exponent.
\[
6^2 = 36
\]
So the expression becomes:
\[
16 + 36 \div 2
\]

3. Division: Perform the division.
\[
36 \div 2 = 18
\]
So the expression becomes:
\[
16 + 18
\]

4. Addition: Perform the addition.
\[
16 + 18 = 34
\]

Final Answer for Problem 8:
\[
\boxed{34}
\]

---

Final Answers:

\[
\boxed{75, 76, -14, 4, 1, 2336, 147, 34}
\]