Class 8 Mathematics

Chapter 2 Solutions — Power Play

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Solutions

Overview

Step-by-step NCERT solutions for Power Play (Chapter 2, NCERT Class 8 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Power Play textbook chapter.

Solved

What these solutions cover

All 17 questions in Power Play are solved in the PDF. Here's what's inside, exercise by exercise:

Exponential Notation and Operations

1.
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
2.
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
3.
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

A Pinch of History — Powers of 10 and Large Numbers

Find out the units digit in the value of 2²²⁴ ÷ 4³²? [Hint: 4 = 2²]
There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?
3.
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)
4.
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…
5.
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) m⁵n¹²(mn)⁹
6.
If 12² = 144 what is
- (i) (1.2)²
- (ii) (0.12)²
- (iii) (0.012)²
- (iv) 120²
Circle the numbers that are the same — 2⁴ × 3⁶ 6⁴ × 3² 6¹⁰ 18² × 6² 6²⁴
8.
Identify the greater number in each of the following —
- (i) 4³ or 3⁴
- (ii) 2⁸ or 8²
- (iii) 100² or 2¹⁰⁰
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?
64 is a square number (8²) and a cube number (4³). Are there other numbers that are both squares and cubes? Is there a way to describe such numbers in general?
A digital locker has an alphanumeric (it can have both digits and letters) passcode of length 5. Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?
12.
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
13.
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…
What was the date 1 arab/1 billion seconds ago?

Sample

Worked examples

3 questions from Power Play, solved step by step.

A Pinch of History — Powers of 10 and Large Numbers

Find out the units digit in the value of 2²²⁴ ÷ 4³²? [Hint: 4 = 2²]

Using the hint, 4 = 2², so 4³² = (2²)³² = 2⁶⁴.

2²²⁴ ÷ 4³² = 2²²⁴ ÷ 2⁶⁴ = 2^(224 – 64) = 2¹⁶⁰.

Find the units digit of 2¹⁶⁰.

Powers of 2 have a units digit cycle of period 4: 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16 (units digit 6), then repeats.

Cycle: 2, 4, 8, 6 (period 4).

160 ÷ 4 = 40 remainder 0.

A remainder of 0 corresponds to the 4th position in the cycle, which has units digit 6.

(Verify: 2⁴ = 16 ends in 6; 2⁸ = 256 ends in 6; the pattern holds.)

Answer: Units digit is 6

A Pinch of History — Powers of 10 and Large Numbers

There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?

Each day, one new container with 5 bottles is brought in.

After 40 days, 40 containers have been brought in.

Total bottles = 40 × 5 = 200.

In exponential form: 200 = 2 × 10².

Answer: 200 bottles (= 2 × 10²)

A Pinch of History — Powers of 10 and Large Numbers

If 12² = 144 what is (i) (1.2)² (ii) (0.12)² (iii) (0.012)² (iv) 120²

Key idea: scale the base, then scale the result by the same factor squared.

(i) (1.2)²

1.2 = 12 ÷ 10, so (1.2)² = (12 ÷ 10)² = 12² ÷ 10² = 144 ÷ 100 = 1.44

(ii) (0.12)²

0.12 = 12 ÷ 100, so (0.12)² = 12² ÷ 100² = 144 ÷ 10000 = 0.0144

(iii) (0.012)²

0.012 = 12 ÷ 1000, so (0.012)² = 12² ÷ 1000² = 144 ÷ 1000000 = 0.000144

(iv) 120²

120 = 12 × 10, so 120² = (12 × 10)² = 12² × 10² = 144 × 100 = 14400

Answer: (i) 1.44 (ii) 0.0144 (iii) 0.000144 (iv) 14400

All 17 questions in Power Play are solved step by step in the Solutions PDF above.

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Chapter 2 Solutions — Power Play

Overview

What these solutions cover

Exponential Notation and Operations

A Pinch of History — Powers of 10 and Large Numbers

Worked examples

Find out the units digit in the value of 2²²⁴ ÷ 4³²? [Hint: 4 = 2²]

There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days?

If 12² = 144 what is (i) (1.2)² (ii) (0.12)² (iii) (0.012)² (iv) 120²

More solutions in Ganita Prakash

More NCERT Solutions for Class 8