CLASS 8 CHAPTER 2 POWER PLAY SOLUTIONS GANITA PRAKASH NCERT

Class 8 – Ganita Prakash

Chapter 2: Power Play – Full Answers with Explanations

🧠 2.1 Experiencing the Power Play

Thickness after 30 folds:
0.001 × 2³⁰ = 0.001 × 1,073,741,824 = 10.7 km

Thickness after 46 folds:
0.001 × 2⁴⁶ ≈ 703,687.4 km (Can reach the Moon!)

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📘 2.2 Exponential Notation and Operations

1. Express in exponential form:

• 6 × 6 × 6 × 6 = 6⁴
• y × y = y²
• b × b × b × b = b⁴
• 5 × 5 × 7 × 7 × 7 = 5² × 7³
• 2 × 2 × a × a = 2² × a²
• a × a × a × c × c × c × c × d = a³ × c⁴ × d

2. Prime factorisation:

• 648 = 2³ × 3⁴
• 405 = 3⁴ × 5
• 540 = 2² × 3³ × 5
• 3600 = 2⁴ × 3² × 5²

3. Numerical Values:

• 2 × 10³ = 2000
• 7² × 2³ = 392
• 3 × 4⁴ = 768
• (–3)² × (–5)² = 9 × 25 = 225
• 3² × 10⁴ = 9 × 10000 = 90,000
• (–2)⁵ × (–10)⁶ = –32,000,000

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💎 The Stones that Shine

Total diamonds = 3⁷ = 2187

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🧮 Properties of Exponents

• p⁴ × p⁶ = p¹⁰
• (4³)² = 4⁶ = 4096
• (2²)⁵ = 2¹⁰ = 1024
• (na)^b = n^a×b

Examples:

• 8⁶ = (2³)⁶ = 2¹⁸
• 7¹⁵ = (7⁵)³ or (7³)⁵
• 9¹⁴ = (3²)¹⁴ = 3²⁸

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🌸 Magical Pond

Day 30 = fully covered → Day 29 = half covered

Tripling pond after 4 days:
2⁴ × 3⁴ = 16 × 81 = 1296 lotuses

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👚 How Many Combinations

• Estu: 4 dresses × 3 caps = 12 combinations
• Roxie: 7 × 2 × 3 = 42 combinations
• 5-digit password: 10⁵ = 100,000
• 6-letter lock (A–Z): 26⁶ = 308,915,776

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✂️ 2.3 The Other Side of Powers

• n^a ÷ n^b = n^a–b
• n⁰ = 1 (n ≠ 0)
• n⁻ᵃ = 1/n^a

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🔬 2.4 Powers of 10 & Scientific Notation

Examples:

• 59,853 = 5.9853 × 10⁴
• 70,04,00,00,000 = 7.004 × 10¹⁰
• Earth–Sun = 1.496 × 10¹¹ m
• Moon = 3.844 × 10⁸ m → Need 3.844 × 10¹³ sheets of paper to reach

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📐 2.5 Did You Ever Wonder?

• Jaggery worth = 45 × ₹70 = ₹3,150
• Wheat worth = 50 × ₹50 = ₹2,500
• 1-rupee coins = 45,000 ÷ 4.8 ≈ 9,375 coins

Number of ladder steps to moon: 3,84,400 km ÷ 0.2 m = 1.922 × 10⁹ steps

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🧠 Figure It Out (Final Questions)

1. Bottles after 40 days:

5 × 40 = 200 bottles

2. 64³ – Different exponential forms:

• (2⁶)³ = 2¹⁸
• (8²)³ = 8⁶

3. True or False:

• Cube numbers are square numbers – Sometimes
• Fourth powers are square – Always
• Fifth power divisible by cube – Always
• Product of two cubes is a cube – Always
• q⁴⁶ is both 4th and 6th power (q is prime) – Yes

4. Simplify in exponential form:

• 10⁻² × 10⁻⁵ = 10⁻⁷
• 57 ÷ 54 = 5³ = 125
• 9⁻⁷ ÷ 9⁴ = 9⁻¹¹
• (13⁻²)⁻³ = 13⁶
• m⁵n¹²(mn)⁹ = m¹⁴n²¹

5. 122 = 144 ⇒ Then:

• (1.2)² = 1.44
• (0.12)² = 0.0144
• (0.012)² = 0.000144
• 120² = 14400

6. Scientific Calculations:

• World clothing = 8.2 × 10⁹ × 30 = 2.46 × 10¹¹
• Bee colonies = 100 million × 50,000 = 5 × 10⁹ × 5 × 10⁴ = 2.5 × 10¹⁴
• Bacteria in humans = 3.12 × 10²³
• Time spent eating = ~1.05 × 10⁸ seconds

7. Date 1 billion seconds ago from August 2025:

Approximately December 1993

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Prepared by: [KEYTOENJOYLEARNINGMATHS] – Based on NCERT Class 8 Chapter 2: Power Play