Power Play Class 8 Maths Worksheet with Answers Chapter 2

Ganita Prakash Part-I, Grade 8, Textbook of Mathematics – Now lets have a look at the 2nd chapter which is, Power Play. The 2nd chapter from the NCERT Ganita Prakash Part-I book is related to chapter 1, which you might have already completed. Do not try to solve these questions until you complete them. The worksheet has 4 sections: Basic, Standard, Advanced, and HOTS. Answers are provided at the bottom for each.

Class 8 Maths Worksheet – Chapter 2: Power Play

Basic

1. Write in exponential form:
   1. 6 × 6 × 6 × 6
   2. y × y
   3. 5 × 5 × 7 × 7 × 7
2. Evaluate:
   1. 5⁴
   2. 2¹⁰
   3. (−3)³
3. Find the sign (positive/negative) and value:
   1. (−1)⁵
   2. (−1)⁵⁶
4. A sheet has initial thickness v. It is folded 10 times. Which expression represents the final thickness?
5. Write 32400 as a product of prime factors and then in exponential form.
6. Answer:
   1. 0² = ?
   2. 0⁵ = ?
   3. 0ⁿ = ? (for any natural number n)

Standard

1. Simplify using laws of exponents: 2⁵ × 5⁵
2. Simplify: 10⁷ ÷ 10³
3. Write 8⁶ as a “power of a power” in two different ways.
4. Simplify: 7³ × 7⁻⁵
5. Write 561.903 in expanded form using powers of 10.
6. Write these numbers in expanded form using powers of 10:
   1. 172
   2. 5642
   3. 6374

Advance

1. Write in scientific notation:
   1. 5900
   2. 0.00072
2. Compute and write the final answer in scientific notation:
   
   (3.2 × 10⁵) × (4 × 10⁻³)
3. Compute and write the final answer in scientific notation:
   
   (6 × 10⁹) ÷ (2.4 × 10³)
4. How many times larger is 4² than 4⁻²?
5. Simplify and write with positive exponents only:
   
   (5⁻² × 5⁷) ÷ 5³
6. Halley’s comet period is about 2.4 × 10⁹ seconds. Approximate this in years.
   
   (Take 1 year ≈ 3.15 × 10⁷ seconds.)

HOTS

1. Magical Pond (Doubling): The number of lotuses doubles every day. The pond is fully covered on the 30th day.
   1. On which day was it half covered?
   2. What fraction was covered on the 29th day?
   3. Write the number of lotuses in exponential form when it was fully covered and half covered (take 1 lotus on Day 1).
2. Two ponds: One pond doubles daily and the other triples daily. Start with 1 lotus in the doubling pond. After 4 days, move all lotuses to the tripling pond, then let it grow for 4 more days. How many lotuses will there be finally?
3. Combinations: Estu has 4 dresses and 3 caps.
   1. How many outfit combinations are possible?
   2. If Estu also has 2 pairs of shoes, how many total combinations now?
4. The number of stars in a galaxy is 1,00,00,00,00,000. Write this number in scientific notation.
5. If you count 1 star per second, how long (in seconds and then in years) will it take to count all the stars in that galaxy?
   
   (Take 1 year ≈ 3.15 × 10⁷ seconds.)
6. Simplify completely:
   
   (3⁴ × 2⁻²) ÷ 6²

Answer Key

Basic – Answers

1. 1. Ans: 6⁴
   2. Ans: y²
   3. Ans: 5² × 7³
2. 1. Ans: 625
   2. Ans: 1024
   3. Ans: −27
3. 1. Ans: (−1)⁵ = −1 (negative)
   2. Ans: (−1)⁵⁶ = +1 (positive)
4. Ans: 2¹⁰v
5. Ans: 32400 = 2⁴ × 3⁴ × 5²
6. 1. Ans: 0² = 0
   2. Ans: 0⁵ = 0
   3. Ans: 0ⁿ = 0 (for n ∈ N)

Standard – Answers

1. Ans: 2⁵ × 5⁵ = (2×5)⁵ = 10⁵
2. Ans: 10⁷ ÷ 10³ = 10⁴
3. Ans: 8⁶ = (8²)³ = (8³)²
4. Ans: 7³ × 7⁻⁵ = 7⁻² = 1/7² = 1/49
5. Ans: 561.903 = (5 × 10²) + (6 × 10¹) + (1 × 10⁰) + (9 × 10⁻¹) + (0 × 10⁻²) + (3 × 10⁻³)
6. 1. Ans: 172 = (1 × 10²) + (7 × 10¹) + (2 × 10⁰)
   2. Ans: 5642 = (5 × 10³) + (6 × 10²) + (4 × 10¹) + (2 × 10⁰)
   3. Ans: 6374 = (6 × 10³) + (3 × 10²) + (7 × 10¹) + (4 × 10⁰)

Advance – Answers

1. 1. Ans: 5900 = 5.9 × 10³
   2. Ans: 0.00072 = 7.2 × 10⁻⁴
2. Ans: (3.2 × 10⁵)(4 × 10⁻³) = 12.8 × 10² = 1.28 × 10³
3. Ans: (6 × 10⁹) ÷ (2.4 × 10³) = (6/2.4) × 10⁶ = 2.5 × 10⁶
4. Ans: 4² ÷ 4⁻² = 4²⁻(−2) = 4⁴ = 256
5. Ans: (5⁻² × 5⁷) ÷ 5³ = 5⁵ ÷ 5³ = 5² = 25
6. Ans: (2.4 × 10⁹) ÷ (3.15 × 10⁷) ≈ (2.4/3.15) × 10² ≈ 0.7619 × 10² ≈ 76 years (approx.)

HOTS – Answers

1. 1. Ans: Half covered on the 29th day.
   2. Ans: On the 29th day it is 1/2 covered.
   3. Ans: If Day 1 has 1 lotus, then Day 30 has 2²⁹ lotuses (fully covered) and Day 29 has 2²⁸ lotuses (half covered).
2. Ans: After 4 days doubling: 2⁴ = 16 lotuses. Then 4 days tripling: 16 × 3⁴ = 16 × 81 = 1296 (= 6⁴).
3. 1. Ans: 4 × 3 = 12 combinations.
   2. Ans: 4 × 3 × 2 = 24 combinations.
4. Ans: 1,00,00,00,00,000 = 10¹¹ (so scientific notation: 1 × 10¹¹).
5. Ans: Time = 10¹¹ seconds. In years: (10¹¹) ÷ (3.15 × 10⁷) ≈ (1/3.15) × 10⁴ ≈ 0.317 × 10⁴ ≈ 3.17 × 10³ years (≈ 3170 years).
6. Ans: (3⁴ × 2⁻²) ÷ 6² = (81 × 1/4) ÷ 36 = (81/4) × (1/36) = 81/144 = 9/16

Worksheet From Other Chapters

Ganita Prakash Part-I

• A Square and a Cube Class 8 Maths Worksheet with Answers
• A Story of Numbers Class 8 Maths Worksheet with Answers
• Number Play Class 8 Maths Worksheet with Answers
• We Distribute, Yet Things Multiply Class 8 Maths Worksheet with Answers
• Proportional Reasoning-1 Class 8 Maths Worksheet with Answers

Ganita Prakash Part-II

• Fractions in Disguise Class 8 Maths Worksheet with Answers
• Proportional Reasoning–2 Class 8 Maths Worksheet with Answers
• Algebra Play Class 8 Maths Worksheet with Answers