Important Questions Class 8 Maths Chapter 2 Power Play 2026-2027

Power Play teaches students how repeated multiplication becomes a power. It explains exponents, exponential growth, powers of 10, scientific notation and large-number reasoning.

Important Questions Class 8 Maths Chapter 2 help students revise exponential notation, laws of exponents, zero power, negative powers, scientific notation, combinations and large-number estimates. This chapter is useful because powers help students read very large and very small numbers without counting every zero.

Class 8 Maths Chapter 2 begins with a surprising paper-folding idea. A thin paper of thickness 0.001 cm doubles after every fold. After 10 folds, it becomes just above 1 cm. After 30 folds, it reaches around 10.7 km. After 46 folds, the thickness becomes more than 7,00,000 km.

This example shows exponential growth. In this chapter, students learn how powers express repeated multiplication in a short form. They also learn how exponent rules simplify calculations, how scientific notation writes large numbers clearly, and how estimation helps compare real-world quantities.

Key Takeaways from Class 8 Maths Chapter 2

Important Questions Class 8 Maths Chapter 2 with Answers

These questions cover the main concepts of the chapter. Students should write the repeated multiplication form before using exponent rules.

Important Questions Class 8 Maths Chapter 2: Power Play Basics

Q1. What is exponential notation?

Exponential notation is a short way to write repeated multiplication.

For example:

5^4 = 5 × 5 × 5 × 5

Here, 5 is the base and 4 is the exponent.

Q2. What is the base in (5^4)?

The base is 5.

The base tells which number gets multiplied repeatedly.

Q3. What is the exponent in (5^4)?

The exponent is 4.

It tells how many times the base is multiplied by itself.

Q4. What is exponential growth?

Exponential growth happens when a quantity multiplies by a fixed factor again and again.

In the paper-folding example, thickness doubles after each fold. So, after (n) folds, the thickness becomes:

0.001 × 2^n

Q5. What is the thickness of paper after 10 folds if the initial thickness is 0.001 cm?

The thickness after 10 folds is:

0.001 × 2^(10)

= 0.001 × 1024

= 1.024 { cm}

So, the paper becomes 1.024 cm thick.

Exponents Class 8 Maths Important Questions

Exponents class 8 maths questions help students avoid long multiplication. Powers also make large growth easier to understand.

Class 8 Maths Chapter 2 Question Answer on Exponential Notation

Q1. Express (6 × 6 × 6 × 6) in exponential form.

The number 6 appears 4 times.

6 × 6 × 6 × 6 = 6^4

Q2. Express (y × y) in exponential form.

y × y = y^2

This is read as (y) squared.

Q3. Express (5 × 5 × 7 × 7 × 7) in exponential form.

Group the repeated factors.

5 × 5 = 5^2

7 × 7 × 7 = 7^3

So:

5 × 5 × 7 × 7 × 7 = 5^2 × 7^3

Q4. Express (a × a × a × c × c × c × c × d) in exponential form.

a × a × a = a^3

c × c × c × c = c^4

So, the expression is:

a^3c^4d

Q5. Express 32400 as a product of prime factors in exponential form.

Prime factorisation:

32400 = 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3 × 3 × 3

So:

32400 = 2^4 × 5^2 × 3^4

Laws of Exponents Class 8 Important Questions

Laws of exponents class 8 questions help students simplify products and quotients quickly. These rules work when the bases match.

Power Play Class 8 Exponent Laws

Q1. State the product law of exponents.

When the bases are the same, add the powers.

n^a × n^b = n^(a+b)

For example:

2^4 × 2^3 = 2^7

Q2. Simplify (p^4 × p^6).

Use:

n^a × n^b = n^(a+b)

p^4 × p^6 = p^(4+6)

= p^(10)

Q3. State the power of a power law.

When a power is raised to another power, multiply the exponents.

(n^a)^b = n^(ab)

For example:

(4^3)^2 = 4^6

Q4. Write (8^6) as power of a power in two ways.

One way:

8^6 = (8^2)^3

Another way:

8^6 = (8^3)^2

Both are correct because:

2 × 3 = 6

Q5. State the quotient law of exponents.

When the bases are the same, subtract the powers.

n^a div n^b = n^(a-b)

where (n ≠ 0).

For example:

2^(10) div 2^5 = 2^5

Class 8 Maths Chapter 2 Question Answer on Zero and Negative Powers

Zero and negative powers often confuse students. The main idea is simple: zero power gives 1 for a non-zero base, and negative powers show reciprocals.

Q1. What is (x^0)?

x^0 = 1

where (x ≠ 0).

This comes from:

x^a div x^a = x^(a-a) = x^0

Any non-zero number divided by itself is 1.

Q2. Why is (0^0) not used here?

The rule (x^0 = 1) works only when (x ≠ 0).

Division by zero is not allowed. So, (0^0) does not fit this rule in this chapter.

Q3. What is (2^(-1))?

A negative power means reciprocal.

2^(-1) = (1)/(2)

Q4. What is (2^(-6))?

2^(-6) = (1)/(2^6)

= (1)/(64)

Q5. Write (10^(-3)) in fraction form.

10^(-3) = (1)/(10^3)

= (1)/(1000)

Scientific Notation Class 8 Important Questions

Scientific notation class 8 questions are important because they help students write very large and very small numbers clearly. This reduces mistakes with zeros.

Q1. What is scientific notation?

Scientific notation writes a number as:

x × 10^y

where (1 ≤ x < 10), and (y) is an integer.

For example:

5900 = 5.9 × 10^3

Q2. Write 59,853 in scientific notation.

Move the decimal after the first digit.

59853 = 5.9853 × 10^4

So, the scientific notation is:

5.9853 × 10^4

Q3. Write 65,950 in scientific notation.

65950 = 6.595 × 10^4

Q4. Write 34,30,000 in scientific notation.

34,30,000 = 3430000

= 3.43 × 10^6

Q5. Write 70,04,00,00,000 in scientific notation.

70,04,00,00,000 = 70040000000

= 7.004 × 10^(10)

Powers of 10 Class 8 Maths Questions

Powers of 10 class 8 questions help students read place value and compare large quantities. They also form the base of scientific notation.

Q1. Write 47561 using powers of 10.

47561 = 4 × 10^4 + 7 × 10^3 + 5 × 10^2 + 6 × 10^1 + 1 × 10^0

Q2. Write 172 using powers of 10.

172 = 1 × 10^2 + 7 × 10^1 + 2 × 10^0

Q3. Write 5642 using powers of 10.

5642 = 5 × 10^3 + 6 × 10^2 + 4 × 10^1 + 2 × 10^0

Q4. Write 561.903 using powers of 10.

561.903 = 5 × 10^2 + 6 × 10^1 + 1 × 10^0 + 9 × 10^(-1) + 0 × 10^(-2) + 3 × 10^(-3)

Q5. Why are powers of 10 useful for large numbers?

Powers of 10 show the size of a number quickly.

For example:

2 × 10^7

means 2 crore. The exponent 7 tells how large the number is.

Exponential Growth Class 8 Important Questions

Exponential growth class 8 questions show how repeated multiplication grows faster than repeated addition. This chapter uses folded paper and lotus growth to make the idea clear.

Q1. How does paper folding show exponential growth?

Each fold doubles the thickness of the paper.

So, if the starting thickness is 0.001 cm, the thickness after (n) folds is:

0.001 × 2^n

This is exponential growth because multiplication repeats.

Q2. How thick is the paper after 30 folds?

From the chapter, after 30 folds, the thickness is about 10.7 km.

This is close to the typical height at which planes fly.

Q3. Why is a pond half full on the 29th day if it is full on the 30th day?

The lotuses double every day.

So, one day before the pond becomes full, it must be half full. Therefore, it is half full on the 29th day.

Q4. A lotus doubles for 4 days and then triples for 4 days. Write the total lotuses in exponential form.

Starting with 1 lotus, after 4 days of doubling:

2^4

After 4 days of tripling:

2^4 × 3^4

Use:

m^a × n^a = (mn)^a

2^4 × 3^4 = 6^4

Q5. What is the difference between linear growth and exponential growth?

Linear growth adds a fixed amount each time.

Exponential growth multiplies by a fixed factor each time. A ladder to the Moon grows linearly by step height, while folded paper grows exponentially by doubling.

Class 8 Maths Chapter 2 Extra Questions with Answers

Class 8 maths chapter 2 extra questions help students practise simplification, comparison and application.

Q1. Simplify (2^(-4) × 2^7).

Use:

n^a × n^b = n^(a+b)

2^(-4) × 2^7 = 2^(-4+7)

= 2^3

= 8

Q2. Simplify (3^2 × 3^(-5) × 3^6).

3^2 × 3^(-5) × 3^6 = 3^(2-5+6)

= 3^3

= 27

Q3. Simplify (p^3 × p^(-10)).

p^3 × p^(-10) = p^(3-10)

= p^(-7)

= (1)/(p^7)

where (p ≠ 0).

Q4. Simplify (10^(-2) × 10^(-5)).

10^(-2) × 10^(-5) = 10^(-7)

= (1)/(10^7)

Q5. Simplify (5^7 div 5^4).

5^7 div 5^4 = 5^(7-4)

= 5^3

= 125

Q6. Simplify ((13^(-2))^(-3)).

Use:

(n^a)^b = n^(ab)

(13^(-2))^(-3) = 13^((-2)(-3))

= 13^6

Combination Questions from Power Play Class 8

Combinations in this chapter show how powers count choices. Passwords, outfits and codes use the same multiplication idea.

Q1. Estu has 4 dresses and 3 caps. How many combinations are possible?

For each dress, there are 3 cap choices.

4 × 3 = 12

So, 12 combinations are possible.

Q2. Roxie has 7 dresses, 2 hats and 3 pairs of shoes. How many combinations are possible?

Multiply the choices.

7 × 2 × 3 = 42

So, 42 combinations are possible.

Q3. How many 5-digit passwords are possible using digits 0 to 9?

Each digit has 10 choices.

10 × 10 × 10 × 10 × 10 = 10^5

= 1,00,000

So, 1,00,000 passwords are possible.

Q4. How many passwords are possible with 6 slots using letters A to Z?

Each slot has 26 choices.

26^6 = 30,89,15,776

So, 30,89,15,776 passwords are possible.

Q5. How many alphanumeric passcodes of length 5 are possible?

Assume each slot can have 10 digits or 26 English letters.

Total choices per slot:

10 + 26 = 36

Total passcodes:

36^5 = 6,04,66,176

So, 6,04,66,176 passcodes are possible.

Application-Based Questions on Exponents Class 8 Maths

Application questions help students understand why powers are useful outside textbook calculations. These questions connect exponents with growth, codes and estimates.

Q1. A bacteria population doubles every hour. If it starts with 3 bacteria, how many bacteria are there after 5 hours?

Each hour, the population doubles.

3 × 2^5

= 3 × 32

= 96

So, there are 96 bacteria after 5 hours.

Q2. A machine makes 10 packets every second. How many packets can it make in (10^4) seconds?

10 × 10^4 = 10^5

So, it can make:

1,00,000

packets.

Q3. A storage device has (2^(10)) units of space. What is the value of (2^(10))?

2^(10) = 1024

So, the storage device has 1024 units of space.

Q4. Why do scientists use scientific notation for distance and mass?

Scientific notation writes very large or very small values compactly.

This helps avoid mistakes while reading zeros, comparing numbers and doing calculations.

Q5. Why does exponential growth feel surprising?

Exponential growth starts slowly but becomes very large after repeated multiplication.

The paper-folding example shows this clearly because each fold doubles the thickness.

Class 8 Maths Chapter 2 MCQs with Answers

Class 8 Maths Chapter 2 MCQs test base, exponent, exponent laws, zero power, negative powers and scientific notation.

Q1. In (7^5), the base is:

(a) 5

(b) 7

(c) 12

(d) 35

Answer: (b) 7

The base is the repeated factor.

Q2. In (7^5), the exponent is:

(a) 7

(b) 5

(c) 35

(d) 12

Answer: (b) 5

The exponent tells how many times the base is multiplied.

Q3. (2^4 × 2^3) equals:

(a) (2^1)

(b) (2^7)

(c) (4^7)

(d) (2^(12))

Answer: (b) (2^7)

Same bases are multiplied by adding exponents.

Q4. (10^0) equals:

(a) 0

(b) 1

(c) 10

(d) 100

Answer: (b) 1

Any non-zero number raised to power 0 is 1.

Q5. (2^(-3)) equals:

(a) 8

(b) -8

(c) ((1)/(8))

(d) (-(1)/(8))

Answer: (c) ((1)/(8))

A negative exponent gives the reciprocal.

Q6. Scientific notation of 80,00,000 is:

(a) (8 × 10^5)

(b) (8 × 10^6)

(c) (8 × 10^7)

(d) (80 × 10^6)

Answer: (b) (8 × 10^6)

80,00,000 equals 8 million.

Competency-Based Questions on Power Play Class 8

These questions test whether students can apply exponent ideas in new situations. Students should explain the rule before calculating.

Q1. A student writes (4^3 = 4 × 3). What is wrong?

The student has confused multiplication with repeated multiplication.

The correct meaning is:

4^3 = 4 × 4 × 4

= 64

Q2. Which is larger: (2^(10)) or (10^2)?

2^(10) = 1024

10^2 = 100

So:

2^(10) > 10^2

Q3. Why can (10^(-2)) represent a small number?

A negative exponent gives a reciprocal.

10^(-2) = (1)/(10^2)

= (1)/(100)

So, it represents a small value.

Q4. A number is written as (6.8 × 10^9). Is it in scientific notation?

Yes, it is in scientific notation.

The coefficient 6.8 lies between 1 and 10, and the power of 10 shows the size of the number.

Q5. A number is written as (45 × 10^3). Is it in scientific notation?

No, it is not in proper scientific notation.

The coefficient should be less than 10. The correct form is:

4.5 × 10^4

Class 8 Maths Important Questions Chapter-Wise