Power Play Class 8 Worksheet with Answers Maths Chapter 2

Each of our Ganita Prakash Class 8 Worksheet and Class 8 Maths Chapter 2 Power Play Worksheet with Answers Pdf focuses on conceptual clarity.

Class 8 Maths Chapter 2 Power Play Worksheet with Answers Pdf

Power Play Class 8 Maths Worksheet

Class 8 Maths Chapter 2 Worksheet with Answers – Class 8 Power Play Worksheet

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Question 1.
A bookshelf has 1 book on Day 1. The number of books doubles every day. On which day will the bookshelf have 16 books?
(a) 3rd day
(6) 4th day
(c) 5th day
(d) 6th day

Question 2.
If a population of bacteria triples every hour, and initially there are 2 bacteria, how many will be there after 3 hours?
(a) 6
(b) 18
(c) 54
(d) 8

Question 3.
In the expression 8⁵, what is the base?
(a) 5
(b) 13
(c) 8
(d) 85

Question 4.
Each vehicle number plate has 3 letters followed by 2 digits. If each letter can be any of 26 alphabets and each digit can be 0 – 9, how many different number plates are possible?
(a) 26³ × 10³
(b) 26³ × 10²
(c) 26² × 10³
(d) 26⁵ × 10⁵

Question 5.
Evaluate: (2 × 5)³
(a) 2³ + 5³ = 13³
(b) 2 × 5³ = 250
(c) 10³ = 1000
(d) 2³ × 5 = 40

Question 6.
Which of the following represents 5 × 5 × 5 × 5 in exponential notation?
(a) 5³
(b) 5⁴
(c) 4⁵
(d) 5 × 4

Question 7.
A sheet of paper has a thickness of 0.002 cm. If it is folded 12 times, what will be its thickness after 12 folds?
(a) 0.002 × 12
(b) 0.002 × 2¹²
(c) 0.002 + 12
(d) 0.002¹²

Question 8.
A bacteria culture triples every hour. If there is 1 bacterium initially, how many bacteria will be there after 4 hours?
(a) 3⁴ = 81
(b) 4³ = 64
(c) 3 × 4 = 12
(d) 4 × 3 = 12

Question 9.
A pond has 0.002 m² of leaves covered on Day 5? on Day 1. The area covered doubles every day. What area will be
(a) 0.032 m²
(6) 0.064 m²
(c) 0.128 m²
(d) 0.016 m²

Question 10.
Simplify: 10⁶ ÷ 10²
(a) 10⁴
(b) 10⁸
(c) 10³
(d) 10⁴

Question 11.
If (x²)³ = x⁶, which property of exponents is being used?
(a) Multiplication of powers with the same base
(b) Division of powers with the same base
(c) Power of a power
(d) Power of a product

Question 12.
The standard form for 0.000000243 is
(a) 24.3 × 10⁶
(b) 2.43 × 10⁷
(c) 24.3 × 10^-8
(d) 2.43 × 10^-7

Question 13.
Exponential growth is a process in which the quantity increases by:
(a) A fixed difference
(b) A fixed ratio or multiple
(c) A random number each time
(d) A constant subtraction

Question 14.
The distance between the Earth and the Moon is approximately 3,84,400 km. If each step of a ladder adds 20 cm, the growth is:
(a) Exponential
(b) Linear
(c) Random
(d) Constant ratio-based

Question 15.
Which ancient Indian treatise gives a list with a name for each power of ten up to 1096?
(a) Ganita-sara-sangraha
(b) Amalasiddhi
(c) Lalitavistara
(d) Pali grammar of Kaccayana

Question 16.
The decimal number 561.903 can be written in expanded form using powers of 10 as:
(a) 5 × 10³ + 6 × 10² + 1 × 10¹ + 9 × 10^-1 + 3 × 10^-3
(b) 5 × 10² + 6 × 101 + 1 × 10° + 9 × 10^-1 + 0 × 10^-2 + 3 × 10^-3
(c) 5 × 10 + 6 × 10¹ + 1 × 10° + 9 × 10¹ + 3 × 10³
(d) 5 × 10^-2 + 6 × 10^-1 + 1 × 10° + 9 × 10¹ + 3 × 10³

Question 17.
A thousand million is called a billion in which number system?
(a) Indian System
(b) American/International System
(c) Ancient Jaina System
(d) Buddhist System

Question 18.
The distance between the Sun and the Earth is 1,49,60,00,00,000 m. Its correct expression standard form is:
(a) 1.496 × 10¹⁰ m
(b) 14.96 × 10¹⁰ m
(c) 1.496 × 10¹¹ m
(d) 1.496 × 10¹² m

Question 19.
Linear growth is best described as a process where the quantity increases by:
(a) A fixed amount in each step
(b) A fixed multiple in each step
(c) Doubling in each step
(d) A random amount in each time

Question 20.
In the “ladder to the Moon” example, linear growth is represented by:
(a) 20+ 20 + 20 + …………
(b) 20 × 20 × 20…
(c) 0.20 + 0.02 + 0.002…..
(d) 20² + 20³ + 20⁴

Question 21.
A number is written in scientific notation as x × 10y. Which of the following is true for coefficient x?
(а) x must be a positive integer
(b) x > 1 and x ≤ 10
(c) 1 ≤ x < 10
(d) x can be any real number if y is an integer

Assertion Reason Questions

In questions 1-4, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Question 1.
Assertion (A) : 2⁵ × 2³ = 2⁸
Reason (R) : When the bases are the same, we add the exponents while multiplying powers,
(a ) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Question 2.
Assertion (A) : (3)² = 3⁸.
Reason (R) : While raising a power to another power, we multiply the exponents.
(а) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Question 3.
Assertion (A) : 5° = 1
Reason (R) : The zero exponent rule states that any non-zero number raised to the power 0 equals 1.
(a) Both ( A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Question 4.
Assertion (A) : (2 × 3)⁴ = 2⁴ × 3⁴
Reason (R) : The power of a product is equal to the product of the powers of its factors.
(a) Both (A) and (R) are true and (R) is the correct explanation of (A).
(b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
(c) (A) is true but (R) is false.
(d) (A) is false but (R) is true.

Fill in the blanks

1. If the paper is folded 5 times, the thickness increases by a factor of ___________, which is written as ___________ in exponential form.
2. The expression 2ⁿ represents a quantity that ___________ every time the value of n increases by 1.
3. Sara has 4 notebooks, 3 pens, and 2 pencil boxes. Number of different stationery sets which Sara can make by choosing one of each are ___________.
4. If the length of a wire is 2 cm and it is cut into equal halves three times, the remaining length can be written as ___________ in exponential form.
5. (2³)⁴ can be written as ___________.
6. The growth pattern in the Power Play activity is called ___________ growth because the quantity keeps multiplying by the same factor.
7. In the Power Play experiment, the exponential notation helps us write repeated ___________ in a shorter and simpler way.
8. In expanded form, the number 3,700 can be written as 3 × 10³ + 7 × 10² + 0 × 10¹ + 0 × 10°. The power of 10 corresponding to the digit 7 is ___________.
9. The distance between the Sun and Earth is approximately 1.496 × 10¹¹ m. Here, the exponent 11 represents the ___________ of the number.
10. The pattern 2, 4, 6, 8, 10… represents a ___________ growth pattern.
11. Large numbers can be written in a more convenient and compact form called the ___________ form by using powers of 10.
12. The text that provides a list of 24 terms for powers of ten, up to 10²³, is the ___________.
13. In linear growth, the quantity increases by the same ___________ in each time interval, while in exponential growth, it increases by the same.
14. In the Lalitavistara, a Buddhist treatise, number-names were given for odd powers of ten up to ___________.
15. In 1946, Hungary printed a banknote valued at 1 sextillion pengo, but it was never ___________
16. In the modern Indian number system, a hundred crores is called an ___________

Write (T) for true or (F) for false for the given statements

1. Exponential growth occurs when a quantity keeps multiplying by the same factor over equal intervals.
2. A company produces 12 million chips per year. If each chip needs a unique 4-digit numeric ID, 1,00,000 total unique IDs are possible.
3. \(\frac{a^5}{b^2}=\frac{a+a+a+a+a}{b+b}\)
4. After 10 folds, the thickness of the paper becomes 210 times its original thickness.
5. When dividing two powers with the same base, the exponents are multiplied.
6. When writing a number like 561.903 in expanded form using powers of 10, only positive exponents are used. Negative exponents are not required.
7. Writing numbers in scientific notation makes calculations easier, especially when multiplying or dividing very large or very small numbers.
8. A constant ratio between consecutive terms indicates exponential growth.
9. The highest numerical value banknote ever printed was in India.
10. The number 10googo1 is called a googol.
11. In scientific notation, written as x × 10y, the coefficient x must satisfy the condition 1 < x < 10.
12. The number 0.00034 can be written in standard form as 3.4 × 10^-4
13. When writing a large number in standard form, the exponent of 10 must always be a positive integer.
14. Linear growth is faster than exponential growth in the long run.
15. In a linear sequence, the difference between consecutive terms is always the same.

Match the columns

Column ‘A’	Column ‘B’
1. (57 ÷ 56)3	(a) 11,664
2. 5 × 5 × 5 × 5 × 5	(b) a2b2c
3. a × a × b × b × c	(c) 53
4. 24 × 36	(d) 3125

Very Short Answer Type Questions

Question 1.
Write the exponential form of “2 multiplied by itself 8 times.”
Solution:
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Question 2.
If the initial thickness of a paper is 0.001 cm, write the expression for its thickness after 4 folds.
Solution:
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Question 3.
A password uses 4 uppercase letters followed by 2 digits. If letters can repeat, how many possible passwords can be formed?
Solution:
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Question 4.
A bacterial colony triples every hour. If it starts with 200 bacteria, how many will there be after 4 hours?
Solution:
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Question 5.
Simplify:
\(\left(\frac{2}{3}\right)^3 \times\left(\frac{5}{7}\right)^3\)
Solution:
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Question 6.
Find the reciprocal of the following:
\(\left(\frac{1}{3}\right)^3 \times\left(\frac{1}{27}\right)^{-3}\)
Solution:
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Question 7.
What is meant by exponential growth?
Solution:
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Question 8.
In the Power Play experiment, by what factor does the paper’s thickness increase with each fold?
Solution:
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Question 9.
Express 864 in exponential notation.
Solution:
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Question 10.
Riya divides her chocolates equally among her friends. If she repeats this process 3 times, each time halving the number, and she started with 64 chocolates, how many are left after the third sharing?
Solution:
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Question 11.
How does the value of a number in scientific notation change if the exponent is increased by one unit (for example, from 107 to 108)?
Solution:
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Question 12.
How can the whole number 47,561 be written in expanded form using powers of 10?
Solution:
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Question 13.
In exponential growth, if a quantity doubles every hour, how many times will it have grown after 3 hours?
Solution:
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Question 14.
If a population of bacteria doubles every 20 minutes, what is the growth rate per minute?
Solution:
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Question 15.
How many terms for powers of ten, up to 1023, are given by Mahaviracharya in his treatise?
Solution:
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Question 16.
In which year did Zimbabwe print a 100 trillion dollar note?
Solution:
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Question 17.
What type of growth is represented by a constant increase or decrease over equal time intervals?
Solution:
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Question 18.
Write the expanded form of 34,56,00,00,00,000 using powers of 10.
Solution:
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Short Answer Type Questions

Question 1.
A sheet of paper has an initial thickness of 0.002 cm. It is folded 12 times.
(а) Write an exponential expression for its thickness after 12 folds.
(b) Calculate its thickness.
Solution:
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Question 2.
Express the following in exponential form:
(a) 5 × 5 × b × a × a × a × a
(b) p × p × p × q × q × r × r × r × r × r × r
(c) 2⁴ × 4²
(d) 6 × 6 × 6 × 6 × p × p
Solution:
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Question 3.
Which of the following has the largest value?
(a) 0.0001
(b) \(\frac{1}{10000}\)
(c) \(\frac{1}{10^6}\)
(d) \(\frac{1}{10^6}\) × 0.1
Solution:
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Question 4.
When factoring the number 24 into its prime factors, we write 2⁴ = 2³ × 3. Using this method, calculate the value of \(\frac{2^{12} \times 5^2}{2^7 \times 3}\) and identify which law of exponents is applied when simplifying \(\frac{2^{15}}{4^5}\).
Solution:
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Question 5.
If the mass of the Earth is 5.97 × 10²⁴ kg and the mass of the Moon is 7.35 × 10²² kg, which is heavier and by how much?
Solution:
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Question 6.
Express the numbers used in the following facts in scientific notation,
(a) The speed of light is 300000000 m/s.
(b) The distance from the Earth to the Moon is 384400000 m.
Solution:
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Question 7.
A piece of paper is folded in half repeatedly. The thickness of the paper grows with each fold. Is this an example of linear or exponential growth? Justify your answer.
Solution:
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Question 8.
What does the first part of the names million, billion, trillion, etc. (like bi- and tri-) signify?
Solution:
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Question 9.
What is the American/International name for a thousand?
Solution:
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Long Answer Type Questions

Question 1.
A pond has a small patch of lotus leaves that doubles in area every day. If the initial area is 0. 001 m³, express the area after 8 days using exponential notation and calculate its value.
Solution:
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Question 2.
Rahul wants to make a healthy snack. He has 5 types of bread, 4 kinds of spreads, and 3 types of fruit to choose from. Using the principle of multiplication, how many different snack combinations can Rahul make?
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Question 1.
The diameter of a planet is approximately 1.39 × 10⁵ km, and the diameter of a moon is approximately 3.48 × 10³ km. By how many orders of magnitude is the planet’s diameter greater than the moon’s?
Solution:
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Question 2.
In a village, the population increases by 100 people each year. In a neighboring village, the population increases by 10% each year. Which village shows linear growth and which shows exponential growth?
Solution:
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Question 3.
Explain why standard form (scientific notation) is necessary for reading and recording extremely large measurements, such as the mass of the Earth or astronomical distances.
Solution:
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Case Based Questions

Exponential Chain
Radhika is a talented digital artist who sells her work online. She decides to use a unique marketing strategy to promote her latest digital painting, “The Glowing Lotus.” Her plan is to give away the first copy of the painting for free to her friend, Riya. She asks Riya to pass the digital file to 5 more friends, and in turn, each of those friends is asked to pass it to 5 new people, and so on. This creates ‘ a chain of sharing.
The number of people receiving the painting at each step of this chain can be represented using powers of 5.

The Chain:

• Step 1: Radhika gives it to 1 friend (which is 5° people, if we consider it the starting point).
• Step 2: Riya passes it to 5 people (5¹).
• Step 3: Those 5 people each pass it to 5 new people (5²).
• Step 4: The 25 people each pass it to 5 new people (5³).
• And so on, creating a powerful “power line of 5.”

Question 1.
How many people will receive the painting at the 5th step of the sharing chain?
Solution:
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Question 2.
If the chain starts with Radhika giving the painting to Riya (which is considered the 1st step), what exponent of 5 represents the number of people receiving the painting at the 7th step?
Solution:
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Question 3.
What is the total number of people who have received the painting, including Radhika and Riya, up to the end of the 7th step of the chain?
Solution:
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Question 4.
Radhika decides to stop the campaign when the number of people receiving the painting in a single step exceeds 10000. At which step will she stop the campaign?
Solution:
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