Order of Operations Worksheet #6 - Practice problems for simplifying expressions using PEMDAS.

Problem Description:

The image shows a worksheet titled "Order of Operations Worksheet #6." It contains 20 problems involving various arithmetic operations, including addition, subtraction, multiplication, division, exponents, and parentheses. The task is to solve each problem step by step using the correct order of operations (PEMDAS/BODMAS rules).

PEMDAS/BODMAS Rules Recap:

1. Parentheses/Brackets (solve expressions inside parentheses or brackets first)
2. Exponents/Orders (calculate powers and roots next)
3. Multiplication and Division (work from left to right)
4. Addition and Subtraction (work from left to right)

Solution to Each Problem:

#### Problem 1: \( (3^2 + 7) - 1 \)
- Solve the exponent: \( 3^2 = 9 \)
- Add inside the parentheses: \( 9 + 7 = 16 \)
- Subtract: \( 16 - 1 = 15 \)
Answer: \( 15 \)

#### Problem 2: \( (2^3 - 5^2 \times 7) + 1 \)
- Solve the exponents: \( 2^3 = 8 \) and \( 5^2 = 25 \)
- Multiply: \( 25 \times 7 = 175 \)
- Subtract inside the parentheses: \( 8 - 175 = -167 \)
- Add: \( -167 + 1 = -166 \)
Answer: \( -166 \)

#### Problem 3: \( 0^3 \times (2^3 + 7 - 7) + 5 \)
- Solve the exponents: \( 0^3 = 0 \) and \( 2^3 = 8 \)
- Simplify inside the parentheses: \( 8 + 7 - 7 = 8 \)
- Multiply: \( 0 \times 8 = 0 \)
- Add: \( 0 + 5 = 5 \)
Answer: \( 5 \)

#### Problem 4: \( 4 + (9^2 - 7) \times 7 \)
- Solve the exponent: \( 9^2 = 81 \)
- Subtract inside the parentheses: \( 81 - 7 = 74 \)
- Multiply: \( 74 \times 7 = 518 \)
- Add: \( 4 + 518 = 522 \)
Answer: \( 522 \)

#### Problem 5: \( (9^3 + 5) - 8^3 + 1 \)
- Solve the exponents: \( 9^3 = 729 \) and \( 8^3 = 512 \)
- Add inside the parentheses: \( 729 + 5 = 734 \)
- Subtract: \( 734 - 512 = 222 \)
- Add: \( 222 + 1 = 223 \)
Answer: \( 223 \)

#### Problem 6: \( (4^2 \times 2^2 + 8) \)
- Solve the exponents: \( 4^2 = 16 \) and \( 2^2 = 4 \)
- Multiply: \( 16 \times 4 = 64 \)
- Add: \( 64 + 8 = 72 \)
Answer: \( 72 \)

#### Problem 7: \( (2 \times 7 \times 8) \)
- Multiply from left to right: \( 2 \times 7 = 14 \), then \( 14 \times 8 = 112 \)
Answer: \( 112 \)

#### Problem 8: \( (5 \times 9 \times 1^2) + 5 \times 2 \)
- Solve the exponent: \( 1^2 = 1 \)
- Multiply inside the parentheses: \( 5 \times 9 \times 1 = 45 \)
- Multiply outside the parentheses: \( 5 \times 2 = 10 \)
- Add: \( 45 + 10 = 55 \)
Answer: \( 55 \)

#### Problem 9: \( (8^2 - 2^3) \times 3 \)
- Solve the exponents: \( 8^2 = 64 \) and \( 2^3 = 8 \)
- Subtract inside the parentheses: \( 64 - 8 = 56 \)
- Multiply: \( 56 \times 3 = 168 \)
Answer: \( 168 \)

#### Problem 10: \( (3 + 5) \times 8 \)
- Add inside the parentheses: \( 3 + 5 = 8 \)
- Multiply: \( 8 \times 8 = 64 \)
Answer: \( 64 \)

#### Problem 11: \( 5^2 \times (7^2 + 7^2) \times 6 \)
- Solve the exponents: \( 5^2 = 25 \), \( 7^2 = 49 \)
- Add inside the parentheses: \( 49 + 49 = 98 \)
- Multiply: \( 25 \times 98 = 2450 \), then \( 2450 \times 6 = 14700 \)
Answer: \( 14700 \)

#### Problem 12: \( (5 \times 3 + 4^2) \div 2 \)
- Solve the exponent: \( 4^2 = 16 \)
- Multiply: \( 5 \times 3 = 15 \)
- Add inside the parentheses: \( 15 + 16 = 31 \)
- Divide: \( 31 \div 2 = 15.5 \)
Answer: \( 15.5 \)

#### Problem 13: \( (5 + 9^2 \times 2^2) - 9 \times 7 \)
- Solve the exponents: \( 9^2 = 81 \) and \( 2^2 = 4 \)
- Multiply: \( 81 \times 4 = 324 \)
- Add inside the parentheses: \( 5 + 324 = 329 \)
- Multiply outside the parentheses: \( 9 \times 7 = 63 \)
- Subtract: \( 329 - 63 = 266 \)
Answer: \( 266 \)

#### Problem 14: \( (1 - 5) - 9^2 + 2 \)
- Solve the exponent: \( 9^2 = 81 \)
- Subtract inside the parentheses: \( 1 - 5 = -4 \)
- Subtract: \( -4 - 81 = -85 \)
- Add: \( -85 + 2 = -83 \)
Answer: \( -83 \)

#### Problem 15: \( 6 + (7^2 + 7) - 6 - 3 = 46 \)
- Solve the exponent: \( 7^2 = 49 \)
- Add inside the parentheses: \( 49 + 7 = 56 \)
- Add and subtract from left to right: \( 6 + 56 = 62 \), then \( 62 - 6 = 56 \), then \( 56 - 3 = 53 \)
Answer: \( 53 \) (Note: The equation provided is incorrect as it states \( = 46 \), but the correct result is \( 53 \).)

#### Problem 16: \( (3 + 4^2 + 8) = 27 \)
- Solve the exponent: \( 4^2 = 16 \)
- Add: \( 3 + 16 = 19 \), then \( 19 + 8 = 27 \)
Answer: \( 27 \)

#### Problem 17: \( 0^2 \times (1 \times 2^2 - 9 \times 8) \)
- Solve the exponents: \( 0^2 = 0 \) and \( 2^2 = 4 \)
- Multiply inside the parentheses: \( 1 \times 4 = 4 \), then \( 9 \times 8 = 72 \)
- Subtract inside the parentheses: \( 4 - 72 = -68 \)
- Multiply: \( 0 \times (-68) = 0 \)
Answer: \( 0 \)

#### Problem 18: \( (8 - 6 + 9) + 3 - 6 \)
- Perform operations from left to right: \( 8 - 6 = 2 \), then \( 2 + 9 = 11 \), then \( 11 + 3 = 14 \), then \( 14 - 6 = 8 \)
Answer: \( 8 \)

#### Problem 19: \( 3 \times (7 - 6) \times 7 \)
- Subtract inside the parentheses: \( 7 - 6 = 1 \)
- Multiply: \( 3 \times 1 = 3 \), then \( 3 \times 7 = 21 \)
Answer: \( 21 \)

#### Problem 20: \( (3^2 + 5^2 + 9) \)
- Solve the exponents: \( 3^2 = 9 \) and \( 5^2 = 25 \)
- Add: \( 9 + 25 = 34 \), then \( 34 + 9 = 43 \)
Answer: \( 43 \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 15 \\
2. & -166 \\
3. & 5 \\
4. & 522 \\
5. & 223 \\
6. & 72 \\
7. & 112 \\
8. & 55 \\
9. & 168 \\
10. & 64 \\
11. & 14700 \\
12. & 15.5 \\
13. & 266 \\
14. & -83 \\
15. & 53 \\
16. & 27 \\
17. & 0 \\
18. & 8 \\
19. & 21 \\
20. & 43 \\
\end{array}
}
\]