Let’s solve each problem step by step using PEMDAS (Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to).
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Problem 1:
6² – (32 – 29)²
→ First, do inside parentheses: 32 – 29 = 3
→ Then exponents: 6² = 36, and 3² = 9
→ Now subtract: 36 – 9 =
27
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Problem 2:
[(21 – 17) × (14 – 9)]²
→ Inner parentheses: 21 – 17 = 4; 14 – 9 = 5
→ Multiply: 4 × 5 = 20
→ Square it: 20² =
400
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Problem 3:
11² – 3 × 8 – 5² – 19
→ Exponents first: 11² = 121; 5² = 25
→ Multiplication: 3 × 8 = 24
→ Now left to right: 121 – 24 = 97; 97 – 25 = 72; 72 – 19 =
53
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Problem 4:
11² – {3 × [8 – (5² – 19)]}
→ Start innermost: 5² = 25 → 25 – 19 = 6
→ Next: 8 – 6 = 2
→ Then: 3 × 2 = 6
→ 11² = 121
→ 121 – 6 =
115
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Problem 5:
11² – [3 × (8 – 5)²] – 19
→ Parentheses: 8 – 5 = 3
→ Exponent: 3² = 9
→ Multiply: 3 × 9 = 27
→ 11² = 121
→ 121 – 27 = 94; 94 – 19 =
75
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Problem 6:
12 × [3 + 11 + 6] – 2³
→ Inside brackets: 3 + 11 + 6 = 20
→ Multiply: 12 × 20 = 240
→ Exponent: 2³ = 8
→ Subtract: 240 – 8 =
232
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Problem 7:
4² + 2⁴ × [40 – (31 – 29)²]
→ Innermost: 31 – 29 = 2 → 2² = 4
→ 40 – 4 = 36
→ Exponents: 4² = 16; 2⁴ = 16
→ Multiply: 16 × 36 = 576
→ Add: 16 + 576 =
592
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Problem 8:
1³ × {9 + [(9 – 21 ÷ 7) – (2⁴ – 5)]}
→ Division first: 21 ÷ 7 = 3 → 9 – 3 = 6
→ Exponent: 2⁴ = 16 → 16 – 5 = 11
→ Inside curly braces: 6 – 11 = -5 → 9 + (-5) = 4
→ 1³ = 1 → 1 × 4 =
4
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Problem 9:
10² × 9 – (4³ – 4 × 10)
→ Exponents: 10² = 100; 4³ = 64
→ Multiplication: 4 × 10 = 40
→ Inside parentheses: 64 – 40 = 24
→ 100 × 9 = 900
→ 900 – 24 =
876
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Problem 10:
4² × 3² – [25 – {2 × (11 + 9 – 13)}]
→ Innermost: 11 + 9 = 20 → 20 – 13 = 7
→ Multiply: 2 × 7 = 14
→ 25 – 14 = 11
→ Exponents: 4² = 16; 3² = 9 → 16 × 9 = 144
→ 144 – 11 =
133
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Final Answer:
27, 400, 53, 115, 75, 232, 592, 4, 876, 133
Parent Tip: Review the logic above to help your child master the concept of advanced algebra worksheet.
