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.

Frequently Asked Questions

What does an exponent tell us about a number?
An exponent tells us how many times a base number is multiplied by itself; for example, in 2 raised to the power 4, the base 2 is multiplied by itself 4 times to give 16.

Last Updated: September 23, 2026

What is the rule for multiplying two powers that have the same base?
When multiplying two powers with the same base, the exponents are added together while the base stays the same, so a raised to power m multiplied by a raised to power n equals a raised to the power m plus n.

Written by Satish

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