Simplify expressions using the PEMDAS rule with this math worksheet.

To solve the problems using the PEMDAS rule (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), we will simplify each expression step by step.

---

Problem 1: \( 20 \div [4 - (10 - 8)] \)

1. Parentheses: Simplify the innermost parentheses first.
\[
10 - 8 = 2
\]
So the expression becomes:
\[
20 \div [4 - 2]
\]

2. Parentheses: Simplify the remaining parentheses.
\[
4 - 2 = 2
\]
So the expression becomes:
\[
20 \div 2
\]

3. Division: Perform the division.
\[
20 \div 2 = 10
\]

Answer: \(\boxed{10}\)

---

Problem 2: \( 9 \times (40 - 29) - (28 - 23) \)

1. Parentheses: Simplify both sets of parentheses.
\[
40 - 29 = 11 \quad \text{and} \quad 28 - 23 = 5
\]
So the expression becomes:
\[
9 \times 11 - 5
\]

2. Multiplication: Perform the multiplication.
\[
9 \times 11 = 99
\]
So the expression becomes:
\[
99 - 5
\]

3. Subtraction: Perform the subtraction.
\[
99 - 5 = 94
\]

Answer: \(\boxed{94}\)

---

Problem 3: \( \{21 - [2 \times (7 + 2^2)]\} + 14 \)

1. Exponents: Simplify the exponent inside the parentheses.
\[
2^2 = 4
\]
So the expression becomes:
\[
\{21 - [2 \times (7 + 4)]\} + 14
\]

2. Parentheses: Simplify the innermost parentheses.
\[
7 + 4 = 11
\]
So the expression becomes:
\[
\{21 - [2 \times 11]\} + 14
\]

3. Multiplication: Perform the multiplication inside the brackets.
\[
2 \times 11 = 22
\]
So the expression becomes:
\[
\{21 - 22\} + 14
\]

4. Parentheses: Simplify the remaining parentheses.
\[
21 - 22 = -1
\]
So the expression becomes:
\[
-1 + 14
\]

5. Addition: Perform the addition.
\[
-1 + 14 = 13
\]

Answer: \(\boxed{13}\)

---

Problem 4: \( 6^2 \div [(-7) - (-5) + 4] \times 9 \)

1. Exponents: Simplify the exponent.
\[
6^2 = 36
\]
So the expression becomes:
\[
36 \div [(-7) - (-5) + 4] \times 9
\]

2. Parentheses: Simplify the expression inside the brackets.
\[
-7 - (-5) = -7 + 5 = -2
\]
So the expression becomes:
\[
36 \div [-2 + 4] \times 9
\]

Next, simplify further inside the brackets:
\[
-2 + 4 = 2
\]
So the expression becomes:
\[
36 \div 2 \times 9
\]

3. Division and Multiplication: Perform the division and multiplication from left to right.
\[
36 \div 2 = 18
\]
So the expression becomes:
\[
18 \times 9
\]

Next, perform the multiplication:
\[
18 \times 9 = 162
\]

Answer: \(\boxed{162}\)

---

Problem 5: \( 8 \times (11 - 3) - (4 \times 9 - 5) \)

1. Parentheses: Simplify both sets of parentheses.
\[
11 - 3 = 8 \quad \text{and} \quad 4 \times 9 - 5 = 36 - 5 = 31
\]
So the expression becomes:
\[
8 \times 8 - 31
\]

2. Multiplication: Perform the multiplication.
\[
8 \times 8 = 64
\]
So the expression becomes:
\[
64 - 31
\]

3. Subtraction: Perform the subtraction.
\[
64 - 31 = 33
\]

Answer: \(\boxed{33}\)

---

Problem 6: \( (12 - 7) \times (33 - 26) - 45 \div 5 \)

1. Parentheses: Simplify both sets of parentheses.
\[
12 - 7 = 5 \quad \text{and} \quad 33 - 26 = 7
\]
So the expression becomes:
\[
5 \times 7 - 45 \div 5
\]

2. Multiplication and Division: Perform the multiplication and division from left to right.
\[
5 \times 7 = 35 \quad \text{and} \quad 45 \div 5 = 9
\]
So the expression becomes:
\[
35 - 9
\]

3. Subtraction: Perform the subtraction.
\[
35 - 9 = 26
\]

Answer: \(\boxed{26}\)

---

Problem 7: \( 2 \times 6 \div (8 - 2) - 2^3 + 3 \times 4 \)

1. Parentheses: Simplify the parentheses.
\[
8 - 2 = 6
\]
So the expression becomes:
\[
2 \times 6 \div 6 - 2^3 + 3 \times 4
\]

2. Exponents: Simplify the exponent.
\[
2^3 = 8
\]
So the expression becomes:
\[
2 \times 6 \div 6 - 8 + 3 \times 4
\]

3. Multiplication and Division: Perform the multiplication and division from left to right.
\[
2 \times 6 = 12 \quad \text{and} \quad 12 \div 6 = 2
\]
So the expression becomes:
\[
2 - 8 + 3 \times 4
\]

Next, perform the remaining multiplication:
\[
3 \times 4 = 12
\]
So the expression becomes:
\[
2 - 8 + 12
\]

4. Addition and Subtraction: Perform the addition and subtraction from left to right.
\[
2 - 8 = -6 \quad \text{and} \quad -6 + 12 = 6
\]

Answer: \(\boxed{6}\)

---

Problem 8: \( [5 + (2^3 \times 4 - (1 + 2)^2)] - 80 \)

1. Exponents: Simplify the exponents.
\[
2^3 = 8 \quad \text{and} \quad (1 + 2)^2 = 3^2 = 9
\]
So the expression becomes:
\[
[5 + (8 \times 4 - 9)] - 80
\]

2. Parentheses: Simplify the expression inside the parentheses.
\[
8 \times 4 = 32 \quad \text{and} \quad 32 - 9 = 23
\]
So the expression becomes:
\[
[5 + 23] - 80
\]

3. Parentheses: Simplify the remaining parentheses.
\[
5 + 23 = 28
\]
So the expression becomes:
\[
28 - 80
\]

4. Subtraction: Perform the subtraction.
\[
28 - 80 = -52
\]

Answer: \(\boxed{-52}\)

---

Problem 9: \( (66 \div 11) \times [26 + (27 \div 9) - 9] \)

1. Parentheses and Division: Simplify the division inside the parentheses.
\[
66 \div 11 = 6 \quad \text{and} \quad 27 \div 9 = 3
\]
So the expression becomes:
\[
6 \times [26 + 3 - 9]
\]

2. Parentheses: Simplify the expression inside the brackets.
\[
26 + 3 = 29 \quad \text{and} \quad 29 - 9 = 20
\]
So the expression becomes:
\[
6 \times 20
\]

3. Multiplication: Perform the multiplication.
\[
6 \times 20 = 120
\]

Answer: \(\boxed{120}\)

---

Problem 10: \( (4^2 \div 2^4) \times [5 + (16 \times 3)] \)

1. Exponents: Simplify the exponents.
\[
4^2 = 16 \quad \text{and} \quad 2^4 = 16
\]
So the expression becomes:
\[
(16 \div 16) \times [5 + (16 \times 3)]
\]

2. Division: Perform the division.
\[
16 \div 16 = 1
\]
So the expression becomes:
\[
1 \times [5 + (16 \times 3)]
\]

3. Parentheses: Simplify the expression inside the brackets.
\[
16 \times 3 = 48 \quad \text{and} \quad 5 + 48 = 53
\]
So the expression becomes:
\[
1 \times 53
\]

4. Multiplication: Perform the multiplication.
\[
1 \times 53 = 53
\]

Answer: \(\boxed{53}\)

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Final Answers

\[
\boxed{10, 94, 13, 162, 33, 26, 6, -52, 120, 53}
\]