NCERT Solutions For Class 8 Maths Chapter 2 Power Play

NCERT Solutions for Class 8 Maths Chapter 2 Power Play helps students understand the concept of powers, exponents, and their real-life applications. This chapter teaches how repeated multiplication can be written in a shorter and smarter form using exponents. Students also learn laws of exponents, standard form, and simplification techniques. These concepts are useful in higher mathematics and competitive exams. Practising the chapter thoroughly helps improve speed, accuracy, and confidence in solving numerical problems.

Important Concepts Covered

  • Powers and Exponents
  • Base and Exponent
  • Laws of Exponents
  • Multiplication and Division of Powers
  • Power of a Power
  • Standard Form
  • Writing Large Numbers in Exponential Form

Formula Revision

  • aᵐ × aⁿ = aᵐ⁺ⁿ
  • aᵐ ÷ aⁿ = aᵐ⁻ⁿ
  • (aᵐ)ⁿ = aᵐⁿ
  • a⁰ = 1

Question & Answers

Q1. Express the following in exponential form:

(i) 6 × 6 × 6 × 6

Answer: 6⁴

NCERT Solutions For Class 8 Maths Chapter 2 Power Play

Power Play (New NCERT)
Medium
Q.
​What is (-1)5? Is it positive or negative? What about (-1)56?​
Power Play (New NCERT)
Medium
Q.
​Find out the units digit in the value of 2224 ÷ 432? [Hint: 4 = 22]​
Power Play (New NCERT)
Medium
Q.
Estu says, “When I become an adult, I would like to donate notebooks worth my weight every year.”
Roxie says, “When I grow up, I would like to do annadana (offering grains or meals) worth my weight every year.”
How many people might benefit from each of these offerings in a year? Again, guess first before finding out.
Power Play (New NCERT)
Medium
Q.
​Roxie and Estu overheard someone saying, “We did a padayatra for about 400 km to reach this place! We arrived early this morning.” How long ago would they have started their journey? Find answers by making necessary assumptions and approximations. Do guess first before calculating to check how close your guess was! ​
Power Play (New NCERT)
Medium
Q.
How many times can a person circumnavigate (go around the world) the Earth in their lifetime, if they walk non-stop? Consider the distance around the Earth as 40,000 km.
Power Play (New NCERT)
Medium
Q.
​Can you come up with some examples of linear growth and of exponential growth?​
Power Play (New NCERT)
Medium
Q.
​With a global human population of about 8 × 109 and about 4 × 105 African elephants, can we say that there are nearly 20,000people for every African elephant? ​
Power Play (New NCERT)
Medium
Q.
Calculate and write the answer using scientific notation. 
With a global human population of about 8 × 109^9​ and about 4 × 105^5​ African elephants, The global chicken population living at any time is estimated at ≈ 33 billion (3.3 × 1010^{10}​). The estimated number of trees (2023) globally stands at 30 kharab/3 trillion (3 × 1012^{12}​). One kharab is 100 arab, and one trillion is 1000 billion. The estimated mosquito population worldwide (2023) is 11 neel/110 trillion. A derived estimate of the population of the Antarctic krill stands at 50 neel/500 trillion (5 × 1014^{14}​). An estimate of the beetle population stands at 1 padma/1 quadrillion (1 × 1015^{15}​). The estimate of the earthworm population is also at 1 padma/1 quadrillion. The estimated population of ants globally is 20 padma/20 quadrillion (2 × 1016^{16}​). Ants alone outweigh all wild birds and wild mammals combined. 1021^{21}​ is supposed to be the number of grains of sand on all beaches and deserts on Earth. The estimated number of stars in the observable universe is 2 × 1023^{23}​. 1025^{25}​ There are an estimated 2 × 1025^{25}​ drops of water on Earth (assuming 16 drops per millilitre).
(i) How many ants are there for every human in the world?
(ii) If a flock of starlings contains 10,000 birds, how many flocks could there be in the world?
(iii) If each tree had about 104^4​ leaves, find the total number of leaves on all the trees in the world.
(iv) If you stacked sheets of paper on top of each other, how many would you need to reach the Moon?​
Power Play (New NCERT)
Medium
Q.
​If you have lived for a million seconds, how old would you be?​
Power Play (New NCERT)
Medium
Q.
105^5​ seconds ~ 1.16 days and 106 seconds ~ 11.57 days. Think of some events or phenomena whose time is of the order of (i) 105 seconds and (ii) 106 seconds. Write them in scientific notation.
Power Play (New NCERT)
Medium
Q.
​The estimated number of stars in the observable universe is 2 × 1023^{23}​. 1025 There are an estimated 2 × 1025^{25}​ drops of water on Earth (assuming 16 drops per millilitre).​
​Calculate and write the answer using scientific notation:
(i) If one star is counted every second, how long would it take to count all the stars in the universe? Answer in terms of the number of seconds using scientific notation.
(ii) If one could drink a glass of water (200 ml) every 10 seconds, how long would it take to finish the entire volume of water on Earth? ​
Power Play (New NCERT)
Medium
Q.
​There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?​
Power Play (New NCERT)
Medium
Q.
​Nanjundappa wants to donate jaggery equal to Roxie’s weight and wheat equal to Estu’s weight. He is wondering how much it would cost.
What would be the worth (in rupees) of the donated jaggery? What would be the worth (in rupees) of the donated wheat? Make necessary and reasonable assumptions for the unknowns and find the answers. Remember, Roxie is 13 years old and Estu is 11 years old.
Power Play (New NCERT)
Medium
Q.
​Write the given number as the product of two or more powers in three different ways. The powers can be any integers.
(i) 643
(ii) 1928
(iii) 32-5​
Power Play (New NCERT)
Medium
Q.
​Examine each statement below and find out if it is ‘Always True’, ‘Only Sometimes True’, or ‘Never True’. Explain your reasoning.
(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 is a prime number).​
Power Play (New NCERT)
Medium
Q.
​Simplify and write these in the exponential form.
(i) 10-2 × 10-5
(ii) 57 ÷ 54
(iii) 9-7 ÷ 94
(iv) (13-2)-3
(v) m5 n12 (mn)9​
Power Play (New NCERT)
Medium
Q.
​If 122 = 144, what is
(i) (1.2)2
(ii) (0.12)2
(iii) (0.012)2
(iv) 1202​
Power Play (New NCERT)
Medium
Q.
​Circle the numbers that are the same
24 × 36,
64 × 32
610
182 × 62
624​
Power Play (New NCERT)
Medium
Q.
​Identify the greater number in each of the following:
(i) 43 or 34
(ii) 28 or 82
(iii) 1002 or 2100​
Power Play (New NCERT)
Medium
Q.
​A dairy plans to produce 8.5 billion packets of milk in a year. They want a unique ID (identifier) code for each packet. If they choose to use the digits 0-9, how many digits should the code consist of?​
Power Play (New NCERT)
Medium
Q.
​A digital locker has an alphanumeric (it can have both digits and letters) pass code of length 5. Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?​
Power Play (New NCERT)
Medium
Q.
​The worldwide population of sheep (2024) is about 109, and that of goats is also about the same. What is the total population of sheep and goats?
(i) 209
(ii) 1011
(iii) 1010
(iv) 1018
(v) 2 × 109
(vi) 109 + 109​
Power Play (New NCERT)
Medium
Q.
​Calculate and write the answer in scientific notation:
(i) If each person in the world had 30 pieces of clothing, find the total number of pieces of clothing.
(ii) There are about 100 million bee colonies in the world. Find the number of honeybees if each colony has about 50,000 bees.
(iii) The human body has about 38 trillion bacterial cells. Find the bacterial population residing in all humans in the world.
(iv) Total time spent eating in a lifetime in seconds.​
Power Play (New NCERT)
Medium
Q.
Assuming Roxie’s weight to be 45 kg and the cost of 1 kg of jaggery to be ₹70, the worth of donated jaggery is 45 × 70 = ₹3150.
Roxie wonders, “Instead of Jaggery, if we use 1-rupee coin, how many coins are needed to equal my weight?” How can we find out?
1. Guessing: Make an instinctive (quick) guess of what the answer could be, without any calculations.
2. Calculating using estimation and approximation —
    (i) Describe the relationships among the quantities that are needed to find the answer. 
    (ii) Make reasonable assumptions and approximations if the required information is not available. 
    (iii) Compute and find the answer (and check how close your guess was).
3. Would the number of coins be in hundreds, thousands, lakhs, crores, or even more? Make an instinctive guess.
4. Estu asks, “What if we use 5-rupee coins or 10-rupee notes instead? How much money could it be?”
Power Play (New NCERT)
Medium
Q.
​Express the following numbers in standard form.
(i) 59,853
(ii) 65,950
(iii) 34,30,000
(iv) 70,04,00,00,000​
Power Play (New NCERT)
Medium
Q.
​Is (-2)4 = 16? Verify.​
Power Play (New NCERT)
Medium
Q.
​Estu and Roxie came across a safe containing old stamps and coins that their great-grandfather had collected. It was secured with a 5-digit password. Since nobody knew the password, they had no option except to try every password until it opened. They were unlucky, and the lock only opened with the last password, after they had tried all possible combinations. How many passwords did they end up checking?
Power Play (New NCERT)
Medium
Q.
​What is 02, 05?​
Power Play (New NCERT)
Medium
Q.
​What is 0n?​
Power Play (New NCERT)
Medium
Q.
​Express the following 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​
Power Play (New NCERT)
Medium
Q.
​Express each of the following as a product of powers of their prime factors in exponential form.
(i) 648
(ii) 405
(iii) 540
(iv) 3600​
Power Play (New NCERT)
Medium
Q.
na×nb=na+bn^a × n^b = n^{a+b}​, where a and b are counting numbers.
​Use this observation to compute the following.
(i) 29
(ii) 57
(iii) 46​
Power Play (New NCERT)
Medium
Q.
​Write the numerical value of each of the following:
(i) 2 × 103
(ii) 72 × 23
(iii) 3 × 44
(iv) (-3)2 × (-5)2
(v) 32 × 104
(vi) (-2)5 × (-10)6​
Power Play (New NCERT)
Medium
Q.
​Write the following expressions as a power of a power in at least two different ways:
(i) 86
(ii) 715
(iii) 914
(iv) 58​
Power Play (New NCERT)
Medium
Q.
In the middle of a beautiful, magical pond lies a bright pink lotus. The number of lotuses doubles every day in this pond. After 30 days, the pond is completely covered with lotuses. 
Write the number of lotuses (in exponential form) when the pond was
(i) fully covered
(ii) half covered
Power Play (New NCERT)
Medium
Q.
Simplify  10454 \;\frac{10^4}{5^4}\;​ and write it in exponential form.
Power Play (New NCERT)
Medium
Q.
​Roxie has 7 dresses, 2 hats, and 3 pairs of shoes. How many different ways can Roxie dress up? ​
Power Play (New NCERT)
Medium
Q.
Estu says, “Next time I will buy a lock that has 6 slots with the letters A to Z. I feel it is safer.” How many passwords are possible with such a lock?
Power Play (New NCERT)
Medium
Q.
​Can you say which of the following distances is the smallest?
​(i) The distance between Sun and Saturn is 1.4335 × 1012 m.
(ii) The distance between Saturn and Uranus is 1.439 × 1012 m.
(iii) The distance between the Sun and Earth is 1.496 × 1011 m.​
Power Play (New NCERT)
Medium
Q.
​Think about how many combinations are possible in different contexts. 
(i) Pin codes of places in India
The Pincode of Vidisha in Madhya Pradesh is 464001.
The Pincode of Zemabawk in Mizoram is 796017.
(ii) Mobile numbers.
(iii) Vehicle registration numbers.
Try to find out how these numbers or codes are allotted/generated.​
Power Play (New NCERT)
Medium
Q.
​What is 2100 ÷ 225 in powers of 2?​
Power Play (New NCERT)
Medium
Q.
​In a generalised form, na ÷ nb = na-b, where n ≠ 0 and a and b are counting numbers and a > b. Why can’t n be 0?​
Power Play (New NCERT)
Medium
Q.
Can we write  103=110−3\;10^3=\frac{1}{10^{-3}}​ ?
Power Play (New NCERT)
Medium
Q.
na÷nb=na–bn^a ÷ n^b = n^{a – b}​, where n ≠ 0 and a and b are counting numbers and a > b.
​We had required a and b to be counting numbers? Can a and b be any integers? Will the generalised forms still hold?​
Power Play (New NCERT)
Medium
Q.
​Write equivalent forms of the following: 
(i) 2-4
(ii) 10-5
(iii) (-7)-2
(iv) (-5)-3
(v) 10-100​
Power Play (New NCERT)
Medium
Q.
​Simplify and write the answers in exponential form.
(i) 2-4 × 27
(ii) 32 × 3-5 × 36
(iii) p3 × p-10
(iv) 24 × (-4)-2
(v) 8p × 8q​
Power Play (New NCERT)
Medium
Q.
​How many times larger than 4-2 is 42? ​
Power Play (New NCERT)
Medium
Q.
 Use the power line for 7 to answer the following questions.
Power Play (New NCERT)
Medium
Q.
Example: 
47561 = (4 × 10000) + (7 × 1000) + (5 × 100) + (6 × 10) + 1.
This can be written using powers of 10 as (4 × 104^4​) + (7 × 103^3 ​) + (5 × 102^2​) + (6 × 101^1​) + (1 × 100^0​)
Write these numbers in the same way: 
(i) 172
(ii) 5642
(iii) 6374​
Power Play (New NCERT)
Medium
Q.
​What was the date 1 arab/1 billion seconds ago?​

NCERT Solutions For Class 8 Maths Chapter 2 Power Play

(ii) y × y

Answer: y²

(iii) b × b × b × b

Answer: b⁴

Q2. Simplify:

(i) 2³ × 2⁴

Answer: 2⁷ = 128

(ii) 5⁶ ÷ 5²

Answer: 5⁴ = 625

Q3. Write in standard form:

(i) 3000000

Answer: 3 × 10⁶

(ii) 0.00045

Answer: 4.5 × 10⁻⁴

Q4. Find the value:

(i) 10²

Answer: 100

(ii) 7⁰

Answer: 1

(iii) 3³

Answer: 27

FAQs

1. What is Chapter 2 of Class 8 Maths?

Chapter 2 of Class 8 Maths is Power Play, based on exponents and powers.

2. Why is this chapter important?

It builds the base for algebra, scientific notation, and higher mathematics.

3. What is exponent?

The exponent tells how many times a number is multiplied by itself.
Example: 2³ = 2 × 2 × 2

4. What is standard form?

A method to write very large or very small numbers using powers of 10.