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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.

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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

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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

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Important Formulas

Exponential Form

$n^a=n\times n\times n\cdots$

Product Rule

$n^a\times n^b=n^{a+b}$

Quotient Rule

$\frac{n^a}{n^b}=n^{a-b}$

Power of a Power

$(n^a)^b=n^{ab}$

Negative Exponent

$n^{-a}=\frac{1}{n^a}$

Scientific Notation

$x\times10^y$

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Questions & Step-by-Step Solutions

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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:

$0.001\times2=0.002$

After second fold:

$0.001\times2^2=0.004$

Final Answer

The thickness becomes double after every fold.

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Q2. What is the thickness after 30 folds?

Solution

Using exponential growth:

$0.001\times2^{30}$

Approximate value:

≈ 10.7 km

Final Answer

The thickness after 30 folds is about 10.7 km.

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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.

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2.2 Exponential Notation and Operations

Q4. Express the following in exponential form

(i) 6 × 6 × 6 × 6

Solution

$6^4$

Answer

6⁴

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(ii) y × y

$y^2$

Answer

y²

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(iii) b × b × b × b

$b^4$

Answer

b⁴

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(iv) 5 × 5 × 7 × 7 × 7

$5^2\times7^3$

Answer

5² × 7³

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Q5. Express 648 in exponential prime factor form

Solution

Prime factorisation:

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

$648=2^3\times3^4$

Final Answer

2³ × 3⁴

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Q6. Find the value of:

(i)

$2\times10^3$

= 2 × 1000

= 2000

Answer

2000

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(ii)

$7^2\times2^3$

= 49 × 8

= 392

Answer

392

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The Stones that Shine

Q7. How many diamonds were there?

Solution

Each level multiplies by 3.

Total diamonds:

$3^7$

= 2187

Final Answer

2187 diamonds.

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Laws of Exponents

Q8. Simplify:

(i)

$p^4\times p^6$

Using product law:

$p^{4+6}=p^{10}$

Final Answer

p¹⁰

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Q9. Write 2¹⁰ as power of power

Solution

$2^{10}=(2^5)^2$

Also,

$2^{10}=(2^2)^5$

Final Answer

(2⁵)² and (2²)⁵

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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.

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Q11. Compute:

$2^5\times5^5$

Solution

Using:

$m^a\times n^a=(mn)^a$

= (2 × 5)⁵

= 10⁵

Final Answer

10⁵

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How Many Combinations

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

Solution

Each slot has 10 choices.

Total combinations:

$10^5$

= 100000

Final Answer

1,00,000 passwords.

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2.3 The Other Side of Powers

Q13. Find:

$2^4\div2^3$

Solution

Using quotient rule:

$2^{4-3}=2^1$

= 2

Final Answer

2

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Q14. What is:

$2^0$

Solution

Any non-zero number raised to zero is 1.

Final Answer

1

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Q15. Find:

$2^{-6}$

Solution

Using negative exponent rule:

$2^{-6}=\frac1{2^6}$​

= 1/64

Final Answer

1/64

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2.4 Powers of 10

Q16. Write 47561 using powers of 10

Solution

$(4\times10^4)+(7\times10^3)+(5\times10^2)+(6\times10^1)+(1\times10^0)$

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

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Scientific Notation

Q17. Express 5900 in scientific notation

Solution

$5900=5.9\times10^3$

Final Answer

5.9 × 10³

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Q18. Express 34,30,000 in standard form

Solution

$3430000=3.43\times10^6$

Final Answer

3.43 × 10⁶

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Large Numbers

Q19. Estimated population of ants

Solution

$2\times10^{16}$

Final Answer

2 × 10¹⁶ ants globally.

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Common Mistakes

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

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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

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Practice MCQs

1. What is 2⁵?

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

Answer

C. 32

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2. Which is equal to 10⁵?

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

Answer

C. 100000

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3. Simplify:

$3^2\times3^4$

A. 3⁶
B. 9⁶
C. 3⁸
D. 6³

Answer

A. 3⁶

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FAQ Section

Q1. What is exponential growth?

Growth that happens through repeated multiplication.

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Q2. What is scientific notation?

A method of writing large numbers using powers of 10.

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

1

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Q4. What is a negative exponent?

It represents reciprocal values.

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Q5. What is the formula for multiplying powers?

$n^a\times n^b=n^{a+b}$

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