Let’s solve each problem step by step using PEMDAS: Parentheses first, then Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right).
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1) 2² × (3² – 4)
→ 3² = 9 → 9 – 4 = 5
→ 2² = 4 → 4 × 5 =
20
Answer: 4 × 5 = 20
2) 10² – (4² + 24)
→ 4² = 16 → 16 + 24 = 40
→ 10² = 100 → 100 – 40 =
60
Answer: 100 – 40 = 60
3) (6² – 2²) × 2
→ 6² = 36, 2² = 4 → 36 – 4 = 32
→ 32 × 2 =
64
Answer: 32 × 2 = 64
4) (2³ + 5²) ÷ 3
→ 2³ = 8, 5² = 25 → 8 + 25 = 33
→ 33 ÷ 3 =
11
Answer: 33 ÷ 3 = 11
5) (3 + 2)²
→ 3 + 2 = 5 → 5² =
25
Answer: 5² = 25
6) (10 – 4)²
→ 10 – 4 = 6 → 6² =
36
Answer: 6² = 36
7) (9 – 7)³ + (2 + 4)²
→ 9 – 7 = 2 → 2³ = 8
→ 2 + 4 = 6 → 6² = 36
→ 8 + 36 =
44
Answer: 8 + 36 = 44
8) (25 – 15)² – 7²
→ 25 – 15 = 10 → 10² = 100
→ 7² = 49 → 100 – 49 =
51
Answer: 100 – 49 = 51
9) (24 ÷ 3)² – 3³
→ 24 ÷ 3 = 8 → 8² = 64
→ 3³ = 27 → 64 – 27 =
37
Answer: 64 – 27 = 37
10) (11 – 3)² – 6²
→ 11 – 3 = 8 → 8² = 64
→ 6² = 36 → 64 – 36 =
28
Answer: 64 – 36 = 28
11) (2.5 + 3.5)² – 5²
→ 2.5 + 3.5 = 6 → 6² = 36
→ 5² = 25 → 36 – 25 =
11
Answer: 36 – 25 = 11
12) 50 – (4.2 + 2.8)²
→ 4.2 + 2.8 = 7 → 7² = 49
→ 50 – 49 =
1
Answer: 50 – 49 = 1
13) 10² – (2³ × 7)
→ 2³ = 8 → 8 × 7 = 56
→ 10² = 100 → 100 – 56 =
44
Answer: 100 – 56 = 44
14) 2 × (3² – 2²)²
→ 3² = 9, 2² = 4 → 9 – 4 = 5
→ 5² = 25 → 2 × 25 =
50
Answer: 2 × 25 = 50
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Now the comparison part:
We compare left side vs right side and put >, <, or =
First one done for you:
(5 + 3)² – 10 = 8² – 10 = 64 – 10 = 54
(5² – 2³) × 3 = (25 – 8) × 3 = 17 × 3 = 51
→ 54 > 51 → Already given.
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Next:
(13 – 7)² ÷ 4 vs
½ × (6² – 4²)
Left: 13 – 7 = 6 → 6² = 36 → 36 ÷ 4 =
9
Right: 6² = 36, 4² = 16 → 36 – 16 = 20 → ½ × 20 =
10
→ 9 < 10 → Answer:
<
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(18 – 3²)² vs
8² + 4² + 1
Left: 3² = 9 → 18 – 9 = 9 → 9² =
81
Right: 8² = 64, 4² = 16 → 64 + 16 + 1 =
81
→ 81 = 81 → Answer:
=
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10² – (3³ × 2) vs
(4 + 3)² – 1³
Left: 3³ = 27 → 27 × 2 = 54 → 10² = 100 → 100 – 54 =
46
Right: 4 + 3 = 7 → 7² = 49 → 1³ = 1 → 49 – 1 =
48
→ 46 < 48 → Answer:
<
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(9 – 5)² + (4 + 3)² vs
(2⁴ + 5) × 3
Left: 9 – 5 = 4 → 4² = 16; 4 + 3 = 7 → 7² = 49 → 16 + 49 =
65
Right: 2⁴ = 16 → 16 + 5 = 21 → 21 × 3 =
63
→ 65 > 63 → Answer:
>
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7² – (5² × 2) vs
(60 – 8²) ÷ 2
Left: 5² = 25 → 25 × 2 = 50 → 7² = 49 → 49 – 50 =
-1
Right: 8² = 64 → 60 – 64 = -4 → -4 ÷ 2 =
-2
→ -1 > -2 → Answer:
>
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Final Answer:
1) 4 × 5 = 20
2) 100 – 40 = 60
3) 32 × 2 = 64
4) 33 ÷ 3 = 11
5) 5² = 25
6) 6² = 36
7) 8 + 36 = 44
8) 100 – 49 = 51
9) 64 – 27 = 37
10) 64 – 36 = 28
11) 36 – 25 = 11
12) 50 – 49 = 1
13) 100 – 56 = 44
14) 2 × 25 = 50
Comparisons:
(13 – 7)² ÷ 4 < ½ × (6² – 4²)
(18 – 3²)² = 8² + 4² + 1
10² – (3³ × 2) < (4 + 3)² – 1³
(9 – 5)² + (4 + 3)² > (2⁴ + 5) × 3
7² – (5² × 2) > (60 – 8²) ÷ 2
Parent Tip: Review the logic above to help your child master the concept of easy pemdas worksheet.
