Simplify expressions using the PEMDAS rule with this math worksheet from Math Monks.

Here are the step-by-step solutions for each problem on the worksheet, following the PEMDAS rule (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

1) $20 \div [4 - (10 - 8)]$
* Step 1: Solve the innermost parentheses first: $(10 - 8) = 2$.
* Equation becomes: $20 \div [4 - 2]$
* Step 2: Solve the brackets: $[4 - 2] = 2$.
* Equation becomes: $20 \div 2$
* Step 3: Divide: $20 \div 2 = 10$.

2) $9 \times (40 - 29) - (28 - 23)$
* Step 1: Solve the first set of parentheses: $(40 - 29) = 11$.
* Step 2: Solve the second set of parentheses: $(28 - 23) = 5$.
* Equation becomes: $9 \times 11 - 5$
* Step 3: Multiply: $9 \times 11 = 99$.
* Equation becomes: $99 - 5$
* Step 4: Subtract: $99 - 5 = 94$.

3) $\{21 - [2 \times (7 + 2^2)]\} + 14$
* Step 1: Solve the exponent inside the parentheses: $2^2 = 4$.
* Equation becomes: $\{21 - [2 \times (7 + 4)]\} + 14$
* Step 2: Solve the addition inside the parentheses: $(7 + 4) = 11$.
* Equation becomes: $\{21 - [2 \times 11]\} + 14$
* Step 3: Solve the multiplication inside the brackets: $[2 \times 11] = 22$.
* Equation becomes: $\{21 - 22\} + 14$
* Step 4: Solve the braces: $\{21 - 22\} = -1$.
* Equation becomes: $-1 + 14$
* Step 5: Add: $-1 + 14 = 13$.

4) $6^2 \div [(-7) - (-5) + 4]^2 \times 9$
* Step 1: Solve the first exponent: $6^2 = 36$.
* Step 2: Simplify inside the brackets. Remember that subtracting a negative is like adding: $(-7) - (-5)$ becomes $-7 + 5 = -2$.
* Then add 4: $-2 + 4 = 2$.
* So, $[(-7) - (-5) + 4] = 2$.
* Step 3: Solve the exponent outside the bracket: $2^2 = 4$.
* Equation becomes: $36 \div 4 \times 9$
* Step 4: Divide and multiply from left to right.
* $36 \div 4 = 9$
* $9 \times 9 = 81$

5) $8 \times (11 - 3) - (4 \times 9 - 5)$
* Step 1: Solve the first parentheses: $(11 - 3) = 8$.
* Step 2: Solve inside the second parentheses. Do multiplication first: $4 \times 9 = 36$. Then subtract: $36 - 5 = 31$.
* Equation becomes: $8 \times 8 - 31$
* Step 3: Multiply: $8 \times 8 = 64$.
* Equation becomes: $64 - 31$
* Step 4: Subtract: $64 - 31 = 33$.

6) $(12 - 7) \times (33 - 26) - 45 \div 5$
* Step 1: Solve the first parentheses: $(12 - 7) = 5$.
* Step 2: Solve the second parentheses: $(33 - 26) = 7$.
* Equation becomes: $5 \times 7 - 45 \div 5$
* Step 3: Do multiplication and division from left to right.
* $5 \times 7 = 35$
* $45 \div 5 = 9$
* Equation becomes: $35 - 9$
* Step 4: Subtract: $35 - 9 = 26$.

7) $2 \times 6 \div (8 - 2) - 2^3 + 3 \times 4$
* Step 1: Solve parentheses: $(8 - 2) = 6$.
* Step 2: Solve exponents: $2^3 = 8$.
* Equation becomes: $2 \times 6 \div 6 - 8 + 3 \times 4$
* Step 3: Do multiplication and division from left to right.
* $2 \times 6 = 12$
* $12 \div 6 = 2$
* $3 \times 4 = 12$
* Equation becomes: $2 - 8 + 12$
* Step 4: Add and subtract from left to right.
* $2 - 8 = -6$
* $-6 + 12 = 6$

8) $\{5 + [2^3 \times 4 - (1 + 2)^2]\} - 80$
* Step 1: Solve innermost parentheses: $(1 + 2) = 3$.
* Step 2: Solve exponents.
* $2^3 = 8$
* $3^2 = 9$ (from the previous step)
* Equation inside brackets becomes: $[8 \times 4 - 9]$
* Step 3: Solve inside the brackets. Multiply first: $8 \times 4 = 32$. Then subtract: $32 - 9 = 23$.
* Equation becomes: $\{5 + 23\} - 80$
* Step 4: Solve braces: $5 + 23 = 28$.
* Equation becomes: $28 - 80$
* Step 5: Subtract: $28 - 80 = -52$.

9) $(66 \div 11) \times [26 + (27 \div 9) - 9]$
* Step 1: Solve the first parentheses: $66 \div 11 = 6$.
* Step 2: Solve inside the brackets. First, do the division inside the inner parentheses: $27 \div 9 = 3$.
* Brackets become: $[26 + 3 - 9]$
* Step 3: Finish the brackets: $26 + 3 = 29$, then $29 - 9 = 20$.
* Equation becomes: $6 \times 20$
* Step 4: Multiply: $6 \times 20 = 120$.

10) $(4^2 \div 2^4) \times [5 + (16 \times 3)]$
* Step 1: Solve exponents in the first part: $4^2 = 16$ and $2^4 = 16$.
* First parentheses become: $(16 \div 16) = 1$.
* Step 2: Solve inside the brackets. Do multiplication first: $16 \times 3 = 48$.
* Brackets become: $[5 + 48] = 53$.
* Step 3: Multiply the results: $1 \times 53 = 53$.

Final Answer:
1) 10
2) 94
3) 13
4) 81
5) 33
6) 26
7) 6
8) -52
9) 120
10) 53