Math worksheet focusing on using parentheses and exponents, with problems that require applying the PEMDAS rule. The sheet includes 14 equations and a comparison section, designed for educational practice.

I'll solve this worksheet step by step, working through each problem carefully.

Let me start with the first section (problems 1-14):

Problem 1: 2² × (3² - 4)
- First: 3² = 9, so (3² - 4) = (9 - 4) = 5
- Then: 2² = 4
- So: 4 × 5 = 20
Answer: 2² × (3² - 4) = 4 × 5 = 20

Problem 2: 10² - (4² + 24)
- First: 4² = 16, so (4² + 24) = (16 + 24) = 40
- Then: 10² = 100
- So: 100 - 40 = 60
Answer: 10² - (4² + 24) = 100 - 40 = 60

Problem 3: (6² - 2²) × 2
- First: 6² = 36 and 2² = 4, so (6² - 2²) = (36 - 4) = 32
- Then: 32 × 2 = 64
Answer: (6² - 2²) × 2 = 32 × 2 = 64

Problem 4: (2³ + 5²) ÷ 3
- First: 2³ = 8 and 5² = 25, so (2³ + 5²) = (8 + 25) = 33
- Then: 33 ÷ 3 = 11
Answer: (2³ + 5²) ÷ 3 = 33 ÷ 3 = 11

Problem 5: (3 + 2)²
- First: (3 + 2) = 5
- Then: 5² = 25
Answer: (3 + 2)² = 5² = 25

Problem 6: (10 - 4)²
- First: (10 - 4) = 6
- Then: 6² = 36
Answer: (10 - 4)² = 6² = 36

Problem 7: (9 - 7)³ + (2 + 4)²
- First: (9 - 7) = 2, so (9 - 7)³ = 2³ = 8
- Second: (2 + 4) = 6, so (2 + 4)² = 6² = 36
- Then: 8 + 36 = 44
Answer: (9 - 7)³ + (2 + 4)² = 8 + 36 = 44

Problem 8: (25 - 15)² - 7²
- First: (25 - 15) = 10, so (25 - 15)² = 10² = 100
- Second: 7² = 49
- Then: 100 - 49 = 51
Answer: (25 - 15)² - 7² = 100 - 49 = 51

Problem 9: (24 ÷ 3)² - 3³
- First: (24 3) = 8, so (24 ÷ 3)² = 8² = 64
- Second: 3³ = 27
- Then: 64 - 27 = 37
Answer: (24 ÷ 3)² - 3³ = 64 - 27 = 37

Problem 10: (11 - 3)² - 6²
- First: (11 - 3) = 8, so (11 - 3)² = 8² = 64
- Second: 6² = 36
- Then: 64 - 36 = 28
Answer: (11 - 3)² - 6² = 64 - 36 = 28

Problem 11: (2.5 + 3.5)² - 5²
- First: (2.5 + 3.5) = 6, so (2.5 + 3.5)² = 6² = 36
- Second: 5² = 25
- Then: 36 - 25 = 11
Answer: (2.5 + 3.5)² - 5² = 36 - 25 = 11

Problem 12: 50 - (4.2 + 2.8)²
- First: (4.2 + 2.8) = 7, so (4.2 + 2.8)² = 7² = 49
- Then: 50 - 49 = 1
Answer: 50 - (4.2 + 2.8)² = 50 - 49 = 1

Problem 13: 10² - (2³ × 7)
- First: 2³ = 8, so (2³ × 7) = (8 × 7) = 56
- Second: 10² = 100
- Then: 100 - 56 = 44
Answer: 10² - (2³ × 7) = 100 - 56 = 44

Problem 14: 2 × (3² - 2²)²
- First: 3² = 9 and 2² = 4, so (3² - 2²) = (9 - 4) = 5
- Second: 5² = 25
- Then: 2 × 25 = 50
Answer: 2 × (3² - 2²)² = 2 × 25 = 50

Now for the comparison section:

Comparison 1: (Already done as example)
(5 + 3)² - 10 > (5² - 2³) × 3
8² - 10 = 54 > (25 - 8) × 3 = 51 ✓

Comparison 2: (13 - 7)² 4 ___ ½ × (6² - 4²)
- Left side: (13 - 7)² ÷ 4 = 6² ÷ 4 = 36 ÷ 4 = 9
- Right side: ½ × (6² - 4²) = ½ × (36 - 16) = ½ × 20 = 10
- So: 9 < 10
Answer: <

Comparison 3: (18 - 3²)² ___ 8² + 4² + 1
- Left side: (18 - 3²)² = (18 - 9)² = 9² = 81
- Right side: 8² + 4² + 1 = 64 + 16 + 1 = 81
- So: 81 = 81
Answer: =

Comparison 4: 10² - (3³ × 2) ___ (4 + 3)² - 1³
- Left side: 10² - (3³ × 2) = 100 - (27 × 2) = 100 - 54 = 46
- Right side: (4 + 3)² - 1³ = 7² - 1 = 49 - 1 = 48
- So: 46 < 48
Answer: <

Comparison 5: (9 - 5)² + (4 + 3)² ___ (2⁴ + 5) × 3
- Left side: (9 - 5)² + (4 + 3)² = 4² + 7² = 16 + 49 = 65
- Right side: (2⁴ + 5) × 3 = (16 + 5) × 3 = 21 × 3 = 63
- So: 65 > 63
Answer: >

Comparison 6: 7² - (5² × 2) ___ (60 - 8²) ÷ 2
- Left side: 7² - (5² × 2) = 49 - (25 × 2) = 49 - 50 = -1
- Right side: (60 - 8²) ÷ 2 = (60 - 64) ÷ 2 = (-4) ÷ 2 = -2
- So: -1 > -2
Answer: >

Final Answer:

Problems 1-14:
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 > (2 + 5) × 3
7² - (5² × 2) > (60 - 8²) ÷ 2