Class 8 Maths Chapter 2 Part 1 Power Play NCERT Solutions (Exponents, Scientific Notation & Growth Explained | Step-by-Step Guide)
Class 8 Maths Chapter 2 Part 1 Power Play NCERT Solutions (Exponents, Scientific Notation & Growth Explained | Step-by-Step Guide)
(Ganita Prakash Part 1)
Introduction
Chapter 2, Power Play, introduces the world of exponents, powers, scientific notation, and exponential growth. Through real-life stories like folding paper, magical ponds, and combinations, students understand how powers grow rapidly and how to express large and small numbers efficiently.
Basic Knowledge Required
• Multiplication
• Factors and prime factorisation
• Place value
• Understanding of repeated multiplication
• Basic algebraic symbols
Important Definitions
1. Exponent / Power
If a number n is multiplied by itself a times, it is written as:
nᵃ = n × n × n × … (a times)
2. Base
The number being multiplied repeatedly (e.g., 5 in 5⁴).
3. Exponential Growth
Growth where a quantity multiplies repeatedly (e.g., doubling, tripling).
4. Scientific Notation
A number written as:
x × 10ⁿ where 1 ≤ x < 10 and n is an integer.
5. Negative Exponents
n⁻ᵃ = 1 / nᵃ
Formulas Used
• nᵃ × nᵇ = nᵃ⁺ᵇ
• (nᵃ)ᵇ = nᵃᵇ
• nᵃ ÷ nᵇ = nᵃ⁻ᵇ
• mᵃ × nᵃ = (mn)ᵃ
• n⁰ = 1
• n⁻ᵃ = 1 / nᵃ
• Scientific notation: x × 10ⁿ
Solved Examples (Step‑by‑Step)
Example 1: Paper Folding (Exponential Growth)
Initial thickness = 0.001 cm
After each fold → thickness doubles
After n folds → 0.001 × 2ⁿ
Example: After 10 folds
0.001 × 2¹⁰ = 0.001 × 1024 = 1.024 cm
Example 2: Express 32400 in exponential form
Prime factorisation:
32400 = 2⁴ × 3⁴ × 5²
Example 3: Evaluate (-2)⁴
(-2) × (-2) × (-2) × (-2) = 16
Example 4: Scientific notation
34,30,000 = 3.43 × 10⁶
Example 5: Power of a Power
(4³)² = 4⁶
FIGURE IT OUT — COMPLETE SOLUTIONS
SECTION 2.1 — Experiencing the Power Play
1. Thickness after folds (Image No. — insert later)
Thickness doubles each time:
0.001 × 2ⁿ
Examples:
18 folds → ≈ 262 cm
19 folds → ≈ 524 cm
20 folds → ≈ 10.4 m
26 folds → ≈ 670 m
30 folds → ≈ 10.7 km
SECTION 2.2 — Exponential Notation
1. Express in exponential form
(i) 6×6×6×6 = 6⁴
(ii) y×y = y²
(iii) b×b×b×b = b⁴
(iv) 5×5×7×7×7 = 5² × 7³
(v) 2×2×a×a = 2² × a²
(vi) a×a×a×c×c×c×c×d = a³ × c⁴ × d
2. Express as product of prime powers
(i) 648 = 2³ × 3⁴
(ii) 405 = 3⁴ × 5
(iii) 540 = 2² × 3³ × 5
(iv) 3600 = 2⁴ × 3² × 5²
3. Numerical values
(i) 2 × 10³ = 2000
(ii) 7² × 2³ = 49 × 8 = 392
(iii) 3 × 4⁴ = 3 × 256 = 768
(iv) (-3)² × (-5)² = 9 × 25 = 225
(v) 3² × 10⁴ = 9 × 10000 = 90000
(vi) (-2)⁵ × (-10)⁶ = -32 × 1,000,000 = -32,000,000
SECTION — The Stones That Shine
1. Total rooms
3⁴ = 81 rooms
2. Total diamonds
3⁷ = 2187 diamonds
SECTION — Magical Pond
1. Pond full & half-full
Full: 2³⁰
Half-full: 2²⁹
2. Tripling pond problem
After 4 days: 2⁴
After next 4 days: 2⁴ × 3⁴ = (2×3)⁴ = 6⁴ = 1296 lotuses
SECTION — How Many Combinations
1. Roxie’s outfits
7 dresses × 2 hats × 3 shoes = 42 combinations
2. 5-digit password
10⁵ = 1,00,000 passwords
3. Lock with letters A–Z
26⁶ combinations
SECTION — The Other Side of Powers
1. 2¹⁰⁰ ÷ 2²⁵
= 2⁷⁵
2. Equivalent forms
2⁻⁴ = 1/2⁴
10⁻⁵ = 1/10⁵
(-7)⁻² = 1/49
(-5)⁻³ = -1/125
SECTION — Powers of 10
Write in expanded powers of 10
(i) 172 = 1×10² + 7×10¹ + 2×10⁰
(ii) 5642 = 5×10³ + 6×10² + 4×10¹ + 2
(iii) 6374 = 6×10³ + 3×10² + 7×10¹ + 4
SECTION — Scientific Notation
Convert to standard form
(i) 59,853 = 5.9853 × 10⁴
(ii) 65,950 = 6.595 × 10⁴
(iii) 34,30,000 = 3.43 × 10⁶
(iv) 70,04,00,00,000 = 7.004 × 10¹⁰
Conclusion
Chapter 2 beautifully connects exponents with real-life situations, helping students understand exponential growth, powers, and scientific notation. These concepts are essential for higher mathematics and science.