Let’s solve each problem step by step, following 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)
→ Inside parentheses: 3² = 9 → 9 - 4 = 5
→ Then exponent: 2² = 4
→ Multiply: 4 × 5 =
20
Answer:
4 × 5 = 20
2) 10² - (4² + 24)
→ Inside parentheses: 4² = 16 → 16 + 24 = 40
→ Then exponent: 10² = 100
→ Subtract: 100 - 40 =
60
Answer:
100 - 40 = 60
3) (6² - 2²) × 2
→ Inside parentheses: 6² = 36, 2² = 4 → 36 - 4 = 32
→ Multiply: 32 × 2 =
64
Answer:
32 × 2 = 64
4) (2³ + 5²) ÷ 3
→ Inside parentheses: 2³ = 8, 5² = 25 → 8 + 25 = 33
→ Divide: 33 ÷ 3 =
11
Answer:
33 ÷ 3 = 11
5) (3 + 2)²
→ Inside parentheses: 3 + 2 = 5
→ Exponent: 5² =
25
Answer:
5² = 25
6) (10 - 4)²
→ Inside parentheses: 10 - 4 = 6
→ Exponent: 6² =
36
Answer:
6² = 36
7) (9 - 7)³ + (2 + 4)²
→ First parentheses: 9 - 7 = 2 → 2³ = 8
→ Second parentheses: 2 + 4 = 6 → 6² = 36
→ Add: 8 + 36 =
44
Answer:
8 + 36 = 44
8) (25 - 15)² - 7²
→ Inside parentheses: 25 - 15 = 10 → 10² = 100
→ 7² = 49
→ Subtract: 100 - 49 =
51
Answer:
100 - 49 = 51
9) (24 ÷ 3)² - 3³
→ Inside parentheses: 24 ÷ 3 = 8 → 8² = 64
→ 3³ = 27
→ Subtract: 64 - 27 =
37
Answer:
64 - 27 = 37
10) (11 - 3)² - 6²
→ Inside parentheses: 11 - 3 = 8 → 8² = 64
→ 6² = 36
→ Subtract: 64 - 36 =
28
Answer:
64 - 36 = 28
11) (2.5 + 3.5)² - 5²
→ Inside parentheses: 2.5 + 3.5 = 6 → 6² = 36
→ 5² = 25
→ Subtract: 36 - 25 =
11
Answer:
36 - 25 = 11
12) 50 - (4.2 + 2.8)²
→ Inside parentheses: 4.2 + 2.8 = 7 → 7² = 49
→ Subtract: 50 - 49 =
1
Answer:
50 - 49 = 1
13) 10² - (2³ × 7)
→ Exponent and inside parentheses: 10² = 100; 2³ = 8 → 8 × 7 = 56
→ Subtract: 100 - 56 =
44
Answer:
100 - 56 = 44
14) 2 × (3² - 2²)²
→ Inside innermost parentheses: 3² = 9, 2² = 4 → 9 - 4 = 5
→ Square that result: 5² = 25
→ Multiply: 2 × 25 =
50
Answer:
2 × 25 = 50
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Now for the comparison section — we calculate both sides and use >, <, or =.
We’re given the first one as example:
(5 + 3)² - 10 = 8² - 10 = 64 - 10 = 54
(5² - 2³) × 3 = (25 - 8) × 3 = 17 × 3 = 51
→ 54 > 51 ✓
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Next: (13 - 7)² ÷ 4 ___ 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 ___ 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) ___ (4 + 3)² - 1³
Left: 10² = 100; 3³ = 27 → 27 × 2 = 54 → 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 ___ (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) ___ (60 - 8²) ÷ 2
Left: 7² = 49; 5² = 25 → 25 × 2 = 50 → 49 - 50 =
-1
Right: 8² = 64 → 60 - 64 = -4 → -4 ÷ 2 =
-2
→ -1 > -2 → Answer:
>
*(Note: Negative numbers — remember, -1 is greater than -2)*
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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 printable pemdas worksheet.
