Class 8 Maths Chapter 2 Power Play Visual Infographic | NCF 2023 Ganita Prakash

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✦ NCF 2023 GANITA PRAKASH • GRADE 8 SERIES ✦

Chapter 2: Power Play

Laws of Exponents, Exponential vs. Linear Growth, Scientific Notation & Ancient Number Systems

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⚡ Laws of Exponents

Product & Quotient Rules

• n^a × n^b = n^a+b
• n^a ÷ n^b = n^a−b (n ≠ 0)

Power of a Power

(n^a)^b = (n^b)^a = n^ab. Powers multiply directly.

Zero & Negative Powers

• n⁰ = 1 (n ≠ 0)
• n^−a = 1 / n^a and n^a = 1 / n^−a

🔬 Scientific Notation & Distributive Powers

1. Distributing Powers:

• m^a × n^a = (mn)^a
• m^a ÷ n^a = (m/n)^a (n ≠ 0)

2. Standard Scientific Form:

Written as x × 10^y, where 1 ≤ x < 10 and y is an integer. The exponent y defines the scale/magnitude.

3. Expanded Place Value with Powers:

561.903 = 5×10² + 6×10¹ + 1×10⁰ + 9×10⁻¹ + 0×10⁻² + 3×10⁻³.

📈 Multiplicative Growth

Paper Folding & Lunar Distance:

A 0.001 cm sheet doubles each fold (thickness = 0.001 × 2^k cm). At 46 folds, thickness exceeds 7,00,000 km (reaching the Moon!).

Linear vs. Exponential:

• Linear: Additive (+20 cm step → 1.92 billion steps to Moon).
• Exponential: Multiplicative (×2 each step → only 46 steps).

Combinations & Permutations:

• 5-digit PIN: 10⁵ = 1,00,000 codes.
• 6-slot letter lock (A-Z): 26⁶ = 308,915,776 combinations.

🏛️ Ancient Indian Number Names & Cosmic Scales

• Indian Number Scale (Powers of 100): Lakh (10⁵), Crore (10⁷), Arab (10⁹), Kharab (10¹¹), Neel (10¹³), Padma (10¹⁵), Shankh (10¹⁷), Maha-shankh (10¹⁹).

• Ancient Buddhist & Jain Texts: Lalitavistara (1st BCE) names powers up to Tallakshana (10⁵³). Amalasiddhi lists up to 10⁹⁶ (Dasha-ananta) and Kāccāyana lists up to 10¹⁴⁰ (Asankhyeya).

• Googol & Googolplex: 1 Googol = 10¹⁰⁰. 1 Googolplex = 10^Googol = 10^(10100). Total atoms in observable universe ≈ 10⁷⁸ to 10⁸².

• Cosmic Time Scales: 10⁹ seconds ≈ 31.7 years. 10¹⁷ seconds ≈ 3.17 billion years. Age of Earth = 4.5 billion years; Age of Universe = 13.8 billion years.

⚠️ Common Exponent Traps

Trap 1: Negative Base vs. Negative Exponent

A negative exponent indicates a reciprocal, NOT a negative answer: 2⁻⁴ = 1/2⁴ = 1/16. Meanwhile, (−2)⁴ = +16 (even power) and (−2)⁵ = −32 (odd power).

Trap 2: Adding Bases When Multiplying

2⁴ × 2³ = 2⁷ (add exponents, keep base same). It is strictly NOT 4⁷! Similarly, 10⁹ + 10⁹ = 2 × 10⁹, NOT 10¹⁸.

Designed by Akash Srivastva | Mathematics Hub • NCF 2023 Visual Learning Series

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