NCERT Solutions for Class 8th Maths Chapter 2 Power Play
Updated on 2026-09-19
About this chapter
n a means n multiplied by itself a times. Here n is the base and a is the exponent (or power). 5 4 = 5 × 5 × 5 × 5 = 625. The five working rules: n a × n b = n a+b , (n a ) b = n ab , n a ÷ n b = n a–b , m a × n a = (mn) a and m a ÷ n a = (m ÷ n) a . n 0 = 1 and n –a = 1/n a (for n ≠ 0) are not extra rules — they are the only definitions that let n a ÷ n b = n a–b keep working when a = b or a Exponential growth multiplies by a fixed factor at each step; linear growth adds a fixed amount. 46 folds reach the Moon, while 192.2 crore ladder steps are needed to do the same job. Scientific notation writes a number as x × 10 y with 1 ≤ x Powers of 10 give names to huge quantities: lakh 10 5 , crore 10 7 , arab 10 9 , kharab 10 11 , neel 10 13 , padma 10 15 ; million 10 6 , billion 10 9 , trillion
- .1 Experiencing the Power Play …
- .2 Exponential Notation and Operations
- .2 Exponential Notation and Operations · Magical Pond
- .3 The Other Side of Powers
- .3 The Other Side of Powers · Power Lines
- .4 Powers of 10
- .4 Powers of 10 · Scientific Notation
- .5 Did You Ever Wonder?
- .5 Did You Ever Wonder? · Getting a Sense for Large Numbers
- .5 Did You Ever Wonder? · A different way to say your age!
Quick revision
| Idea | General form | Example from the chapter | Why it works |
|---|---|---|---|
| Product of powers | na × nb = na+b | 34 × 33 = 37 = 2187 | a factors of n, then b more — a + b factors in all |
| Power of a power | (na)b = (nb)a = na×b | (42)3 = 46 = 4096 | b groups, each with a factors |
| Quotient of powers | na ÷ nb = na–b (n ≠ 0) | 24 ÷ 23 = 21 = 2 | b factors below cancel b factors above |
| Same exponent, two bases | ma × na = (mn)a | 25 × 55 = 105 = 1,00,000 | regroup into a pairs, each pair m × n |
| Division, same exponent | ma ÷ na = (m ÷ n)a (n ≠ 0) | 104 ÷ 54 = 24 = 16 | a fractions m/n multiplied together |
| Zero exponent | n0 = 1 (n ≠ 0) | 40 = 1 | na ÷ na is 1, and the rule calls it n0 |
| Negative exponent | n–a = 1/na (n ≠ 0) | 2–6 = 1/64 | keep halving past n0 and the pattern continues |
| Flipping a negative power | na = 1/n–a | 72 = 1/7–2 | the reciprocal of a reciprocal is the number itself |
| Standard (scientific) form | x × 10y, 1 ≤ x < 10, y an integer | 5900 = 5.9 × 103 | y fixes the size, x fixes the leading digits |
| Exponential vs linear growth | × fixed factor vs + fixed amount | 46 folds vs 1,92,20,00,000 steps | multiplying compounds; adding does not |
| Indian names | lakh 105, crore 107, arab 109, kharab 1011, neel 1013, padma 1015, shankh 1017 | 2 crore = 2 × 107 | each name is 100 times the one before |
| International names | million 106, billion 109, trillion 1012, quadrillion 1015 | 3 trillion trees = 3 × 1012 | each name is 1000 times the one before |
Exercises
- .1 Experiencing the Power Play … — In-text Questions Page 192
- .1 Experiencing the Power Play … — In-text Questions Page 202
- .1 Experiencing the Power Play … — In-text Questions Page 212
- .2 Exponential Notation and Operations — In-text Questions Page 222
- .2 Exponential Notation and Operations — Figure it Out Page 22–232
- .2 Exponential Notation and Operations · The Stones that Shine … — In-text Questions Page 232
- .2 Exponential Notation and Operations — In-text Questions Page 242
- .2 Exponential Notation and Operations · Magical Pond — In-text Questions Page 252
- .2 Exponential Notation and Operations · How Many Combinations — In-text Questions Page 262
- .2 Exponential Notation and Operations · 2.3 The Other Side of Powers — In-text Questions Page 27–282
- .3 The Other Side of Powers — In-text Questions Page 282
- .3 The Other Side of Powers — In-text Questions Page 292
- .3 The Other Side of Powers · Power Lines — In-text Questions Page 302
- .4 Powers of 10 — In-text Questions Page 312
- .4 Powers of 10 · Scientific Notation — In-text Questions Page 322
- .5 Did You Ever Wonder? — In-text Questions Page 33–342
- .5 Did You Ever Wonder? · Linear Growth vs. Exponential Growth — In-text Questions Page 35–362
- .5 Did You Ever Wonder? · Getting a Sense for Large Numbers — In-text Questions Page 37–382
- .5 Did You Ever Wonder? · Getting a Sense for Large Numbers — In-text Questions Page 38–392
- .5 Did You Ever Wonder? · A different way to say your age! — In-text Questions Page 392
- .5 Did You Ever Wonder? — In-text Questions Page 402
- .5 Did You Ever Wonder? — In-text Questions Page 41–422
- .5 A Pinch of History — In-text Questions Page 432
- .5 A Pinch of History (chapter-end set) — Figure it Out Page 44–452
- Puzzle Time! Tremendous in Ten! — In-text Questions Page 47