Revision Notes: Class 8 Maths Chapter 2 Power Play

Class 8 Maths Chapter 2: Power Play — Quick Revision Notes

• Exponential notation: aⁿ = a×a×…×a (n times); a is the base, n is the exponent/power.
• Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ (same base, add exponents).
• Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a≠0, same base, subtract exponents).
• Power of a power: (aᵐ)ⁿ = aᵐⁿ.
• Power of a product/quotient: aᵐ×bᵐ = (ab)ᵐ; aᵐ÷bᵐ = (a÷b)ᵐ (b≠0).
• Zero exponent: a⁰ = 1 for any a≠0 (0⁰ is undefined).
• Negative exponent: a⁻ⁿ = 1/aⁿ, and aⁿ = 1/a⁻ⁿ (a≠0). All exponent laws extend to negative and zero integer exponents.
• Standard (scientific) form: any number written as x×10ᶟ, where 1≤x<10 and y is an integer. Compare exponents first when judging size — the exponent matters more than the coefficient.
• Linear vs exponential growth: exponential (doubling/multiplicative) growth vastly outpaces linear (additive) growth over the same number of steps — e.g. paper folded 46 times reaches the Moon, while walking there step-by-step would take about 192 crore steps.
• Number systems for large numbers: Indian system — lakh=10⁵, crore=10⁷, arab=10⁹, kharab=10¹¹, neel=10¹³, padma=10¹⁵; International system — million=10⁶, billion=10⁹, trillion=10¹², quadrillion=10¹⁵. Googol=10¹⁰⁰.
• Historical note: ancient Indian texts named very large powers of ten early — the Lalitavistara (≈1st century BCE) names odd powers of ten up to 10⁵³, and Mahaviracharya’s Ganita-sara-sangraha lists 24 place-value terms up to 10²³.

Written by Satish

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