Grade 5 Order of Operations Worksheet focusing on PEMDAS with nested parentheses.

Problem: Solve the given expressions using the PEMDAS rule (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

#### Step-by-Step Solutions:

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1. \( 6^2 + (32 - 2 \times 9)^2 = \)

1. Parentheses: Solve the inner expression \( 32 - 2 \times 9 \).
- First, perform multiplication: \( 2 \times 9 = 18 \).
- Then, subtract: \( 32 - 18 = 14 \).
- So, \( (32 - 2 \times 9) = 14 \).

2. Exponents: Calculate \( 6^2 \) and \( 14^2 \).
- \( 6^2 = 36 \)
- \( 14^2 = 196 \)

3. Addition: Add the results: \( 36 + 196 = 232 \).

Answer: \( \boxed{232} \)

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2. \( [(2 + 17) \times (14 - 9)]^2 = \)

1. Parentheses: Solve the inner expressions.
- \( 2 + 17 = 19 \)
- \( 14 - 9 = 5 \)

2. Multiplication: Multiply the results: \( 19 \times 5 = 95 \).

3. Exponents: Square the result: \( 95^2 = 9025 \).

Answer: \( \boxed{9025} \)

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3. \( 1^2 + 3 \times 8 - 5^2 - 19 = \)

1. Exponents: Calculate \( 1^2 \) and \( 5^2 \).
- \( 1^2 = 1 \)
- \( 5^2 = 25 \)

2. Multiplication: Perform \( 3 \times 8 \).
- \( 3 \times 8 = 24 \)

3. Addition and Subtraction: Combine all terms in order.
- \( 1 + 24 - 25 - 19 \)
- \( 1 + 24 = 25 \)
- \( 25 - 25 = 0 \)
- \( 0 - 19 = -19 \)

Answer: \( \boxed{-19} \)

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4. \( 1^2 + [3 \times (8 - (5^2 - 19))] = \)

1. Innermost Parentheses: Solve \( 5^2 - 19 \).
- \( 5^2 = 25 \)
- \( 25 - 19 = 6 \)

2. Next Parentheses: Solve \( 8 - 6 \).
- \( 8 - 6 = 2 \)

3. Multiplication: Multiply \( 3 \times 2 \).
- \( 3 \times 2 = 6 \)

4. Exponents: Calculate \( 1^2 \).
- \( 1^2 = 1 \)

5. Addition: Add the results: \( 1 + 6 = 7 \).

Answer: \( \boxed{7} \)

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5. \( 1^2 - [3 \times (8 - [5^2 - 19])] - 19 = \)

1. Innermost Parentheses: Solve \( 5^2 - 19 \).
- \( 5^2 = 25 \)
- \( 25 - 19 = 6 \)

2. Next Parentheses: Solve \( 8 - 6 \).
- \( 8 - 6 = 2 \)

3. Multiplication: Multiply \( 3 \times 2 \).
- \( 3 \times 2 = 6 \)

4. Exponents: Calculate \( 1^2 \).
- \( 1^2 = 1 \)

5. Subtraction: Subtract step by step.
- \( 1 - 6 = -5 \)
- \( -5 - 19 = -24 \)

Answer: \( \boxed{-24} \)

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6. \( 12 \times (3 + 11 + 6) - 2^3 = \)

1. Parentheses: Solve the inner expression \( 3 + 11 + 6 \).
- \( 3 + 11 = 14 \)
- \( 14 + 6 = 20 \)

2. Multiplication: Multiply \( 12 \times 20 \).
- \( 12 \times 20 = 240 \)

3. Exponents: Calculate \( 2^3 \).
- \( 2^3 = 8 \)

4. Subtraction: Subtract the results: \( 240 - 8 = 232 \).

Answer: \( \boxed{232} \)

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7. \( 4^2 + 2^2 \times [40 - (31 - 29)]^2 = \)

1. Innermost Parentheses: Solve \( 31 - 29 \).
- \( 31 - 29 = 2 \)

2. Next Parentheses: Solve \( 40 - 2 \).
- \( 40 - 2 = 38 \)

3. Exponents: Calculate \( 4^2 \), \( 2^2 \), and \( 38^2 \).
- \( 4^2 = 16 \)
- \( 2^2 = 4 \)
- \( 38^2 = 1444 \)

4. Multiplication: Multiply \( 4 \times 1444 \).
- \( 4 \times 1444 = 5776 \)

5. Addition: Add the results: \( 16 + 5776 = 5792 \).

Answer: \( \boxed{5792} \)

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8. \( 1^3 \times (9 + [(9 - 21 + 7) - (2^3 + 5)]) = \)

1. Innermost Parentheses: Solve \( 9 - 21 + 7 \).
- \( 9 - 21 = -12 \)
- \( -12 + 7 = -5 \)

2. Next Inner Parentheses: Solve \( 2^3 + 5 \).
- \( 2^3 = 8 \)
- \( 8 + 5 = 13 \)

3. Subtraction: Solve \( -5 - 13 \).
- \( -5 - 13 = -18 \)

4. Addition: Solve \( 9 + (-18) \).
- \( 9 - 18 = -9 \)

5. Exponents: Calculate \( 1^3 \).
- \( 1^3 = 1 \)

6. Multiplication: Multiply \( 1 \times (-9) \).
- \( 1 \times (-9) = -9 \)

Answer: \( \boxed{-9} \)

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9. \( 10^2 \times 9 - (4^3 \times 4 \times 10) = \)

1. Exponents: Calculate \( 10^2 \) and \( 4^3 \).
- \( 10^2 = 100 \)
- \( 4^3 = 64 \)

2. Multiplication:
- \( 100 \times 9 = 900 \)
- \( 64 \times 4 = 256 \)
- \( 256 \times 10 = 2560 \)

3. Subtraction: Subtract the results: \( 900 - 2560 = -1660 \).

Answer: \( \boxed{-1660} \)

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10. \( 4^2 + 3^2 - [25 - (2 \times (11 + 9 - 13))] = \)

1. Innermost Parentheses: Solve \( 11 + 9 - 13 \).
- \( 11 + 9 = 20 \)
- \( 20 - 13 = 7 \)

2. Next Parentheses: Solve \( 2 \times 7 \).
- \( 2 \times 7 = 14 \)

3. Subtraction: Solve \( 25 - 14 \).
- \( 25 - 14 = 11 \)

4. Exponents: Calculate \( 4^2 \) and \( 3^2 \).
- \( 4^2 = 16 \)
- \( 3^2 = 9 \)

5. Addition and Subtraction: Combine all terms.
- \( 16 + 9 = 25 \)
- \( 25 - 11 = 14 \)

Answer: \( \boxed{14} \)

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Final Answers:

1. \( \boxed{232} \)
2. \( \boxed{9025} \)
3. \( \boxed{-19} \)
4. \( \boxed{7} \)
5. \( \boxed{-24} \)
6. \( \boxed{232} \)
7. \( \boxed{5792} \)
8. \( \boxed{-9} \)
9. \( \boxed{-1660} \)
10. \( \boxed{14} \)