NCERT Solutions for Class 8 Maths Chapter 2: Power Play – Free PDF Download

Chapter 2 — Power Play — introduces exponents: writing repeated multiplication as powers, the laws of exponents (product, quotient, power-of-a-power, power-of-a-product, zero and negative exponents), and using powers of 10 to express and compare very large or very small numbers in standard (scientific) form. The chapter has two Figure It Out blocks (3 questions + 14 questions = 17 in all). Below are complete, verified answers, sourced directly from the official NCERT PDF and independently recalculated. These Class 8 Mathematics Chapter 2 solutions are also useful as quick revision notes before exams.

NCERT Solutions for Class 8 Maths Chapter 2: Power Play

Figure It Out — Block 1 (Section 2.2)

1. Express in exponential form: (i) 6×6×6×6 (ii) y×y (iii) b×b×b×b (iv) 5×5×7×7×7 (v) 2×2×a×a (vi) a×a×a×c×c×c×c×d
(i) 6⁴ (ii) y² (iii) b⁴ (iv) 5²×7³ (v) 2²×a² (vi) a³×c⁴×d

2. Express as a product of powers of prime factors: (i) 648 (ii) 405 (iii) 540 (iv) 3600
(i) 2³×3⁴ (ii) 3⁴×5 (iii) 2²×3³×5 (iv) 2⁴×3²×5²

3. Write the numerical value: (i) 2×10³ (ii) 7²×2³ (iii) 3×4⁴ (iv) (−3)²×(−5)² (v) 3²×10⁴ (vi) (−2)⁵×(−10)⁶
(i) 2000 (ii) 392 (iii) 768 (iv) 225 (v) 90,000 (vi) −32,000,000

Figure It Out — Block 2 (Sections 2.4–2.5)

1. Find the units digit in 2²²⁴ ÷ 4³² (hint: 4=2²).
4³² = 2⁶⁴, so 2²²⁴÷2⁶⁴ = 2¹⁶⁰. Units digits of powers of 2 cycle every 4 (2,4,8,6); 160÷4 is exact, so the units digit is 6.

2. 5 bottles per container, one new container each day — bottles after 40 days?
40×5 = 200 (= 2×10²).

3. Write as a product of two or more powers, three different ways: (i) 64³ (ii) 192⁸ (iii) 32⁻⁵
(i) 64³ = 2¹⁰×2⁸ = 4⁵×4⁴ = 8³×8³ (all = 2¹⁸). (ii) 192⁸ = 2⁴⁸×3⁸ = 2⁴⁰×2⁸×3⁸ = 2⁴⁰×6⁸. (iii) 32⁻⁵ = 2⁻¹⁰×2⁻¹⁵ = 2⁻⁵×2⁻²⁰ = 4⁻¹²×2⁻¹.

4. Always True / Only Sometimes True / Never True: (i) Cube numbers are also square numbers. (ii) Fourth powers are also square numbers. (iii) The fifth power of a number is divisible by the cube of that number. (iv) The product of two cube numbers is a cube number. (v) q⁴⁶ is both a 4th power and a 6th power (q prime).
(i) Only Sometimes True (true only for 6th powers, e.g. 64=4³=8²). (ii) Always True (n⁴=(n²)²). (iii) Always True (n⁵=n³·n²). (iv) Always True (a³b³=(ab)³). (v) Never True — needs the exponent to be a multiple of lcm(4,6)=12; 46 isn’t divisible by 4 or 6.

5. Simplify: (i) 10⁻²×10⁻⁵ (ii) 5⁷÷5⁴ (iii) 9⁻⁷÷9⁴ (iv) (13⁻²)⁻³ (v) m⁵n¹²(mn)⁹
(i) 10⁻⁷ (ii) 5³ (iii) 9⁻¹¹ (iv) 13⁶ (v) m¹⁴n²¹

6. If 12²=144, find: (i) (1.2)² (ii) (0.12)² (iii) (0.012)² (iv) 120²
(i) 1.44 (ii) 0.0144 (iii) 0.000144 (iv) 14,400

7. Circle the numbers that are equal: 2⁴×3⁶, 6⁴×3², 6¹⁰, 18²×6², 6²⁴
2⁴×3⁶ = 6⁴×3² = 18²×6² = 11,664 (all equal). 6¹⁰ and 6²⁴ are different values.

8. Which is greater? (i) 4³ or 3⁴ (ii) 2⁸ or 8² (iii) 100² or 2¹⁰⁰
(i) 3⁴=81 > 4³=64 → 3⁴. (ii) 2⁸=256 > 8²=64 → 2⁸. (iii) 2¹⁰⁰ (≈1.27×10³⁰) is vastly greater → 2¹⁰⁰.

9. A dairy needs unique IDs for 8.5 billion milk packets/year using digits 0–9. How many digits needed?
10⁹ is too small; 10¹⁰ ≥ 8.5×10⁹ → at least 10 digits.

10. 64 is both a square (8²) and a cube (4³). Are there other such numbers? What’s the rule?
Yes, infinitely many — any 6th power n⁶ is both a square [(n³)²] and a cube [(n²)³]: 1, 64, 729, 4096, 15625…

11. A 5-character passcode uses 26 letters + 10 digits. How many possible codes?
36⁵ = 60,466,176.

12. World sheep population ≈10⁹, goat population ≈10⁹. Which expression(s) give the total? Options: 20⁹, 10¹¹, 10¹⁰, 10¹⁸, 2×10⁹, 10⁹+10⁹
2×10⁹ and 10⁹+10⁹ are correct (both equal the same value); the others are not.

13. Calculate and express in scientific notation: (i) total clothing if everyone owns 30 pieces (world population ≈8.2×10⁹) (ii) total honeybees (≈10⁸ colonies × 50,000 bees) (iii) total bacteria in all humans (≈38 trillion/person) (iv) lifetime seconds spent eating (state your assumptions)
(i) 8.2×10⁹×30 = 2.46×10¹¹ pieces. (ii) 10⁸×5×10⁴ = 5.0×10¹² bees. (iii) 38×10¹²×8.2×10⁹ = 3.116×10²³ bacteria. (iv) Using 1 hour/day, 70-year lifespan: 3600×365×70 ≈ 9.198×10⁷ seconds (reasonable alternative assumptions will give a different but equally valid figure — state your assumptions clearly).

14. What was the date one billion (10⁹) seconds ago?
10⁹ seconds ÷ 31,557,600 seconds/year ≈ 31.7 years before today — work this out from today’s date (this is a live, date-dependent calculation, not a fixed answer).

Selected Math Talk & Try This (In-text) Highlights

Paper-folding: thickness after 10 folds, starting thickness v?
2¹⁰v — each fold doubles the thickness, so n folds give 2ⁿv.

Is (−1)⁵ positive or negative? What about (−1)⁵⁶?
(−1)⁵ = −1 (odd exponent keeps the sign); (−1)⁵⁶ = +1 (even exponent gives a positive result).

What is 0², 0⁵? What is 0ⁿ in general?
0²=0, 0⁵=0; 0ⁿ=0 for every positive integer n. (0⁰ itself is left undefined.)

Simplify 10⁴/5⁴ using the power-of-a-quotient rule.
(10÷5)⁴ = 2⁴ = 16.

Roxie has 7 dresses, 2 hats, 3 pairs of shoes — how many outfit combinations?
7×2×3 = 42 combinations.

Express 59,853; 65,950; 34,30,000; 70,04,00,00,000 in standard (scientific) form.
5.9853×10⁴; 6.595×10⁴; 3.43×10⁶; 7.004×10¹⁰.

Why This Chapter Matters

Exponent laws and scientific notation are used constantly afterward — in expressing large/small measurements in science, in the Baudhayana–Pythagoras Theorem chapter (Part 2), and in algebra, where powers of variables follow the exact same rules introduced here.

More on This Chapter

Extra Questions (HOTS) | Revision Notes | Formulas Handbook | Class 8 Maths Book

Frequently Asked Questions

Is this the same as the old Class 8 Maths ‘Exponents and Powers’ chapter?
The core laws of exponents are the same mathematics, but this is a new chapter (‘Power Play’) in the NEP-aligned Ganita Prakash textbook, with a fresh set of questions, real-world Fermi-estimation problems, and historical/cultural notes not found in the older edition.

Some answers (like Q13–14 in Block 2) depend on assumptions or today’s date — is that a mistake?
No — these are intentional open estimation questions in the NCERT book itself. Any reasonable, clearly stated assumption is considered a correct approach.

Written by Satish

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