NCERT Class 8 Maths Power Play Solutions Guide

Short Introduction

The chapter “Power Play” introduces students to the fascinating world of exponents, exponential growth, scientific notation, powers of 10, and large numbers. Through interesting real-life examples like folding paper, magical ponds, password combinations, and huge world statistics, students learn how powers simplify calculations and help represent extremely large or small numbers.

Quick Information Box

Particular Details
Chapter Name Power Play
Class Grade 8
Subject Mathematics
Main Topics Exponents, Powers, Scientific Notation
Difficulty Level Moderate
Important For School Exams, Olympiads
Skills Developed Logical Thinking, Estimation, Number Sense

Concepts Used (Topics Covered)

  • Exponential Growth
  • Exponential Notation
  • Laws of Exponents
  • Negative Exponents
  • Powers of 10
  • Scientific Notation
  • Large Numbers
  • Linear vs Exponential Growth
  • Estimation & Approximation
  • Real-life Applications of Powers

Important Formulas

Exponential Form

na=n×n×n⋯n^a=n\times n\times n\cdots

Product Rule

na×nb=na+bn^a\times n^b=n^{a+b}

Quotient Rule

nanb=na−b\frac{n^a}{n^b}=n^{a-b}

Power of a Power

(na)b=nab(n^a)^b=n^{ab}

Negative Exponent

n−a=1nan^{-a}=\frac{1}{n^a}

Scientific Notation

x×10yx\times10^y

Questions & Step-by-Step Solutions

2.1 Experiencing the Power Play

Q1. What happens to the thickness after every fold?

Solution

The thickness doubles after every fold.

Initial thickness = 0.001 cm

After first fold:

0.001×2=0.0020.001\times2=0.002

After second fold:

0.001×22=0.0040.001\times2^2=0.004

Final Answer

The thickness becomes double after every fold.

Q2. What is the thickness after 30 folds?

Solution

Using exponential growth:

0.001×2300.001\times2^{30}

Approximate value:

≈ 10.7 km

Final Answer

The thickness after 30 folds is about 10.7 km.

Q3. Why is this called exponential growth?

Solution

The quantity increases by repeated multiplication instead of repeated addition.

After every fold:

×2 growth occurs.

Final Answer

This is called exponential growth because the thickness multiplies repeatedly.

2.2 Exponential Notation and Operations

Q4. Express the following in exponential form

(i) 6 × 6 × 6 × 6

Solution

646^4

Answer

6⁴

(ii) y × y

y2y^2

Answer

y²

(iii) b × b × b × b

b4b^4

Answer

b⁴

(iv) 5 × 5 × 7 × 7 × 7

52×735^2\times7^3

Answer

5² × 7³

Q5. Express 648 in exponential prime factor form

Solution

Prime factorisation:

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

648=23×34648=2^3\times3^4

Final Answer

2³ × 3⁴

Q6. Find the value of:

(i)

2×1032\times10^3

= 2 × 1000

= 2000

Answer

2000

(ii)

72×237^2\times2^3

= 49 × 8

= 392

Answer

392

The Stones that Shine

Q7. How many diamonds were there?

Solution

Each level multiplies by 3.

Total diamonds:

373^7

= 2187

Final Answer

2187 diamonds.

Laws of Exponents

Q8. Simplify:

(i)

p4×p6p^4\times p^6

Using product law:

p4+6=p10p^{4+6}=p^{10}

Final Answer

p¹⁰

Q9. Write 2¹⁰ as power of power

Solution

210=(25)22^{10}=(2^5)^2

Also,

210=(22)52^{10}=(2^2)^5

Final Answer

(2⁵)² and (2²)⁵

Magical Pond

Q10. If pond becomes full on 30th day, when was it half full?

Solution

Since the lotuses double every day:

Half full = one day earlier.

Final Answer

29th day.

Q11. Compute:

25×552^5\times5^5

Solution

Using:

ma×na=(mn)am^a\times n^a=(mn)^a

= (2 × 5)⁵

= 10⁵

Final Answer

10⁵

How Many Combinations

Q12. How many passwords are possible in a 5-digit lock?

Solution

Each slot has 10 choices.

Total combinations:

10510^5

= 100000

Final Answer

1,00,000 passwords.

2.3 The Other Side of Powers

Q13. Find:

24÷232^4\div2^3

Solution

Using quotient rule:

24−3=212^{4-3}=2^1

= 2

Final Answer

2

Q14. What is:

202^0

Solution

Any non-zero number raised to zero is 1.

Final Answer

1

Q15. Find:

2−62^{-6}

Solution

Using negative exponent rule:

2−6=1262^{-6}=\frac1{2^6}​

= 1/64

Final Answer

1/64

2.4 Powers of 10

Q16. Write 47561 using powers of 10

Solution

(4×104)+(7×103)+(5×102)+(6×101)+(1×100)(4\times10^4)+(7\times10^3)+(5\times10^2)+(6\times10^1)+(1\times10^0)

(4 × 10⁴) + (7 × 10³) + (5 × 10²) + (6 × 10¹) + (1 × 10⁰)

Scientific Notation

Q17. Express 5900 in scientific notation

Solution

5900=5.9×1035900=5.9\times10^3

Final Answer

5.9 × 10³

Q18. Express 34,30,000 in standard form

Solution

3430000=3.43×1063430000=3.43\times10^6

Final Answer

3.43 × 10⁶

Large Numbers

Q19. Estimated population of ants

Solution

2×10162\times10^{16}

Final Answer

2 × 10¹⁶ ants globally.

Common Mistakes

  • Confusing multiplication with powers
  • Forgetting exponent rules
  • Writing incorrect scientific notation
  • Ignoring negative exponent meaning
  • Wrong prime factorisation

Exam Tips

  • Memorise exponent laws carefully
  • Practice scientific notation daily
  • Revise powers of 10 frequently
  • Solve estimation-based questions
  • Learn real-life applications of exponents

Practice MCQs

1. What is 2⁵?

A. 10
B. 25
C. 32
D. 64

Answer

C. 32

2. Which is equal to 10⁵?

A. 1000
B. 10000
C. 100000
D. 1000000

Answer

C. 100000

3. Simplify:

32×343^2\times3^4

A. 3⁶
B. 9⁶
C. 3⁸
D. 6³

Answer

A. 3⁶

FAQ Section

Q1. What is exponential growth?

Growth that happens through repeated multiplication.

Q2. What is scientific notation?

A method of writing large numbers using powers of 10.

Q3. What is the value of any number raised to zero?

1

Q4. What is a negative exponent?

It represents reciprocal values.

Q5. What is the formula for multiplying powers?

na×nb=na+bn^a\times n^b=n^{a+b}

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