NCERT Textbook: Power Play | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

 Page 1


2
POWER PLAY
2.1 Experiencing the Power Play ...
An Impossible Venture!
Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold 
it again, and again. 
How many times can you fold it over and over?
Estu says “I heard that a sheet of paper can’t be folded more than  
7 times”.
Roxie replies “What if we use a thinner paper, like a newspaper or a 
tissue paper?”
Try it with different types of paper and see what happens.
Say you can fold a sheet of paper as many times as you wish. What would 
its thickness be after 30 folds? Make a guess.
Let us find out how thick a sheet of paper will be after 46 folds. Assume 
that the thickness of the sheet is 0.001 cm.
If you can fold a paper 
46 times, it will be so 
thick that it can reach 
the Moon!
What! That’s crazy! 
Just 46 times!? You 
must have ignored 
several zeros 
after 46.
Well, why 
don’t you find 
out yourselves.
Chapter 2.indd   19 Chapter 2.indd   19 7/10/2025   3:29:53 PM 7/10/2025   3:29:53 PM
Page 2


2
POWER PLAY
2.1 Experiencing the Power Play ...
An Impossible Venture!
Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold 
it again, and again. 
How many times can you fold it over and over?
Estu says “I heard that a sheet of paper can’t be folded more than  
7 times”.
Roxie replies “What if we use a thinner paper, like a newspaper or a 
tissue paper?”
Try it with different types of paper and see what happens.
Say you can fold a sheet of paper as many times as you wish. What would 
its thickness be after 30 folds? Make a guess.
Let us find out how thick a sheet of paper will be after 46 folds. Assume 
that the thickness of the sheet is 0.001 cm.
If you can fold a paper 
46 times, it will be so 
thick that it can reach 
the Moon!
What! That’s crazy! 
Just 46 times!? You 
must have ignored 
several zeros 
after 46.
Well, why 
don’t you find 
out yourselves.
Chapter 2.indd   19 Chapter 2.indd   19 7/10/2025   3:29:53 PM 7/10/2025   3:29:53 PM
Ganita Prakash | Grade 8 
20
The following table lists the thickness after each fold. Observe that the 
thickness doubles after each fold.
Fold Thickness Fold Thickness Fold Thickness
1 0.002 cm 7 0.128 cm 13 8.192 cm
2 0.004 cm 8 0.256 cm 14 16.384 cm
3 0.008 cm 9 0.512 cm 15 32.768 cm
4 0.016 cm 10 1.024 cm 16 65.536 cm
5 0.032 cm 11 2.048 cm 17 ˜ 131 cm
6 0.064 cm 12 4.096 cm
(We use the sign ‘˜’ to indicate ‘approximately equal to’.)
After 10 folds, the thickness is just above 1 cm (1.024 cm).
After 17 folds, the thickness is about 131 cm (a little more than 4 feet).
Now, what do you think the thickness would be after 30 folds? 
45 folds? Make a guess.
Fill the table below.
Fold Thickness Fold Thickness Fold Thickness
18 ˜ 262 cm 21 24
19 ˜ 524 cm 22 25
20 ˜ 10.4 m 23 26
After 26 folds, the thickness is approximately 670 m. Burj Khalifa 
in Dubai, the tallest building in the world, is 830 m tall.
Fold Thickness Fold Thickness
27 ˜ 1.3 km 29
28 30
After 30 folds, the thickness of the paper is about 10.7 km, the 
typical height at which planes fly. The deepest point discovered in 
the oceans is the Mariana Trench, with a depth of 11 km.
Fold Thickness Fold Thickness Fold Thickness
31 36 41
32 37 42
33 38 43
34 39 44
35 40 45
Math 
Talk
Chapter 2.indd   20 Chapter 2.indd   20 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Page 3


2
POWER PLAY
2.1 Experiencing the Power Play ...
An Impossible Venture!
Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold 
it again, and again. 
How many times can you fold it over and over?
Estu says “I heard that a sheet of paper can’t be folded more than  
7 times”.
Roxie replies “What if we use a thinner paper, like a newspaper or a 
tissue paper?”
Try it with different types of paper and see what happens.
Say you can fold a sheet of paper as many times as you wish. What would 
its thickness be after 30 folds? Make a guess.
Let us find out how thick a sheet of paper will be after 46 folds. Assume 
that the thickness of the sheet is 0.001 cm.
If you can fold a paper 
46 times, it will be so 
thick that it can reach 
the Moon!
What! That’s crazy! 
Just 46 times!? You 
must have ignored 
several zeros 
after 46.
Well, why 
don’t you find 
out yourselves.
Chapter 2.indd   19 Chapter 2.indd   19 7/10/2025   3:29:53 PM 7/10/2025   3:29:53 PM
Ganita Prakash | Grade 8 
20
The following table lists the thickness after each fold. Observe that the 
thickness doubles after each fold.
Fold Thickness Fold Thickness Fold Thickness
1 0.002 cm 7 0.128 cm 13 8.192 cm
2 0.004 cm 8 0.256 cm 14 16.384 cm
3 0.008 cm 9 0.512 cm 15 32.768 cm
4 0.016 cm 10 1.024 cm 16 65.536 cm
5 0.032 cm 11 2.048 cm 17 ˜ 131 cm
6 0.064 cm 12 4.096 cm
(We use the sign ‘˜’ to indicate ‘approximately equal to’.)
After 10 folds, the thickness is just above 1 cm (1.024 cm).
After 17 folds, the thickness is about 131 cm (a little more than 4 feet).
Now, what do you think the thickness would be after 30 folds? 
45 folds? Make a guess.
Fill the table below.
Fold Thickness Fold Thickness Fold Thickness
18 ˜ 262 cm 21 24
19 ˜ 524 cm 22 25
20 ˜ 10.4 m 23 26
After 26 folds, the thickness is approximately 670 m. Burj Khalifa 
in Dubai, the tallest building in the world, is 830 m tall.
Fold Thickness Fold Thickness
27 ˜ 1.3 km 29
28 30
After 30 folds, the thickness of the paper is about 10.7 km, the 
typical height at which planes fly. The deepest point discovered in 
the oceans is the Mariana Trench, with a depth of 11 km.
Fold Thickness Fold Thickness Fold Thickness
31 36 41
32 37 42
33 38 43
34 39 44
35 40 45
Math 
Talk
Chapter 2.indd   20 Chapter 2.indd   20 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Power Play
21
It might be hard to digest the fact that after just 46 folds, the thickness 
is more than 7,00,000 km. This is the power of multiplicative growth, 
also called exponential growth. Let us analyse the growth.
We have seen that the thickness doubles after every fold.
Notice the change in thickness after two 
folds. By how much does it increase?
After any 3 folds, the thickness increases 8 
times (= 2 × 2 × 2). Check if that is true. Similarly, 
from any point, the thickness after 10 folds increases by 1024 times  
(= 2 multiplied by itself 10 times), as shown in the table below.
Fold Thickness Times increased by
0 to 10 1.024 cm – 0.001 cm 
= 1.023 cm
1.024 ÷ 0.001  
= 1024
10 to 20 10.485 m – 1.024 cm 
  ˜ 10.474 m
10.485 m ÷ 1.024 cm 
= 1024
20 to 30 10.737 km – 10.485 m
˜ 10.726 km
10.737 km ÷ 10.485 m
= 1024
30 to 40 10995 km – 10.737 km
 ˜ 10984.2 km
10995 km ÷ 
10.737 km = 1024
2.2 Exponential Notation and Operations
The initial thickness of the paper was 0.001 cm. 
Upon folding once, its thickness became 0.001 cm × 2 = 0.002 cm.
Folding it twice, its thickness became —
0.001 cm × 2 × 2 = 0.004 cm, or 0.001 cm × 2
2
 = 0.004 cm (in shorthand).
Upon folding it thrice, its thickness became —
0.001 cm × 2 × 2 × 2, or 0.001 cm × 2
3
 = 0.008 cm. 
When folded four times, its thickness became —
0.001 cm × 2 × 2 × 2 × 2, or 0.001 cm × 2
4
 = 0.016 cm.
Similarly, the expression for the thickness of the paper when folded 7 
times will be 0.001 cm × 2 × 2 × 2 × 2 × 2 × 2 × 2, or 0.001 cm × 2
7
 = 0.128 cm.
We have seen that square numbers can be expressed as n
2
 and cube 
numbers as n
3
.
n × n = n
2
 (read as ‘n squared’ or ‘n raised to the power 2’)
Fold 4 0.016 cm
Fold 5 0.032 cm
Fold 9 0.512 cm
Fold 10 1.024 cm
Fold 4 0.016 cm
Fold 6 0.064 cm
Chapter 2.indd   21 Chapter 2.indd   21 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Page 4


2
POWER PLAY
2.1 Experiencing the Power Play ...
An Impossible Venture!
Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold 
it again, and again. 
How many times can you fold it over and over?
Estu says “I heard that a sheet of paper can’t be folded more than  
7 times”.
Roxie replies “What if we use a thinner paper, like a newspaper or a 
tissue paper?”
Try it with different types of paper and see what happens.
Say you can fold a sheet of paper as many times as you wish. What would 
its thickness be after 30 folds? Make a guess.
Let us find out how thick a sheet of paper will be after 46 folds. Assume 
that the thickness of the sheet is 0.001 cm.
If you can fold a paper 
46 times, it will be so 
thick that it can reach 
the Moon!
What! That’s crazy! 
Just 46 times!? You 
must have ignored 
several zeros 
after 46.
Well, why 
don’t you find 
out yourselves.
Chapter 2.indd   19 Chapter 2.indd   19 7/10/2025   3:29:53 PM 7/10/2025   3:29:53 PM
Ganita Prakash | Grade 8 
20
The following table lists the thickness after each fold. Observe that the 
thickness doubles after each fold.
Fold Thickness Fold Thickness Fold Thickness
1 0.002 cm 7 0.128 cm 13 8.192 cm
2 0.004 cm 8 0.256 cm 14 16.384 cm
3 0.008 cm 9 0.512 cm 15 32.768 cm
4 0.016 cm 10 1.024 cm 16 65.536 cm
5 0.032 cm 11 2.048 cm 17 ˜ 131 cm
6 0.064 cm 12 4.096 cm
(We use the sign ‘˜’ to indicate ‘approximately equal to’.)
After 10 folds, the thickness is just above 1 cm (1.024 cm).
After 17 folds, the thickness is about 131 cm (a little more than 4 feet).
Now, what do you think the thickness would be after 30 folds? 
45 folds? Make a guess.
Fill the table below.
Fold Thickness Fold Thickness Fold Thickness
18 ˜ 262 cm 21 24
19 ˜ 524 cm 22 25
20 ˜ 10.4 m 23 26
After 26 folds, the thickness is approximately 670 m. Burj Khalifa 
in Dubai, the tallest building in the world, is 830 m tall.
Fold Thickness Fold Thickness
27 ˜ 1.3 km 29
28 30
After 30 folds, the thickness of the paper is about 10.7 km, the 
typical height at which planes fly. The deepest point discovered in 
the oceans is the Mariana Trench, with a depth of 11 km.
Fold Thickness Fold Thickness Fold Thickness
31 36 41
32 37 42
33 38 43
34 39 44
35 40 45
Math 
Talk
Chapter 2.indd   20 Chapter 2.indd   20 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Power Play
21
It might be hard to digest the fact that after just 46 folds, the thickness 
is more than 7,00,000 km. This is the power of multiplicative growth, 
also called exponential growth. Let us analyse the growth.
We have seen that the thickness doubles after every fold.
Notice the change in thickness after two 
folds. By how much does it increase?
After any 3 folds, the thickness increases 8 
times (= 2 × 2 × 2). Check if that is true. Similarly, 
from any point, the thickness after 10 folds increases by 1024 times  
(= 2 multiplied by itself 10 times), as shown in the table below.
Fold Thickness Times increased by
0 to 10 1.024 cm – 0.001 cm 
= 1.023 cm
1.024 ÷ 0.001  
= 1024
10 to 20 10.485 m – 1.024 cm 
  ˜ 10.474 m
10.485 m ÷ 1.024 cm 
= 1024
20 to 30 10.737 km – 10.485 m
˜ 10.726 km
10.737 km ÷ 10.485 m
= 1024
30 to 40 10995 km – 10.737 km
 ˜ 10984.2 km
10995 km ÷ 
10.737 km = 1024
2.2 Exponential Notation and Operations
The initial thickness of the paper was 0.001 cm. 
Upon folding once, its thickness became 0.001 cm × 2 = 0.002 cm.
Folding it twice, its thickness became —
0.001 cm × 2 × 2 = 0.004 cm, or 0.001 cm × 2
2
 = 0.004 cm (in shorthand).
Upon folding it thrice, its thickness became —
0.001 cm × 2 × 2 × 2, or 0.001 cm × 2
3
 = 0.008 cm. 
When folded four times, its thickness became —
0.001 cm × 2 × 2 × 2 × 2, or 0.001 cm × 2
4
 = 0.016 cm.
Similarly, the expression for the thickness of the paper when folded 7 
times will be 0.001 cm × 2 × 2 × 2 × 2 × 2 × 2 × 2, or 0.001 cm × 2
7
 = 0.128 cm.
We have seen that square numbers can be expressed as n
2
 and cube 
numbers as n
3
.
n × n = n
2
 (read as ‘n squared’ or ‘n raised to the power 2’)
Fold 4 0.016 cm
Fold 5 0.032 cm
Fold 9 0.512 cm
Fold 10 1.024 cm
Fold 4 0.016 cm
Fold 6 0.064 cm
Chapter 2.indd   21 Chapter 2.indd   21 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Ganita Prakash | Grade 8 
22
n × n × n = n
3
 (read as ‘n cubed’ or ‘n raised to the power 3’)
n × n × n × n = n
4
 (read as ‘n raised to the power 4’ or ‘the 4th power of n’)
n × n × n × n × n × n × n = n
7
 (read as ‘n raised to the power 7’ or ‘the 7th 
power of n’) and so on.
In general, we write n
a
 to denote n multiplied by itself a times.
        5
4
 
= 5 × 5 × 5 × 5 = 625.
5
4
 is the exponential form of 625. Here, 4 is the 
exponent/power, and 5 is the base. Exponents of 
the form 5
n
 are called powers of 5: 5
1
, 5
2
, 5
3
, 5
4
, etc. 
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2
10
 = 1024. 
Remember the 1024 from earlier? There, it meant 
that after every 10 folds, the thickness increased 
1024 times.
Which expression describes the thickness of a sheet of paper after 
it is folded 10 times? The initial thickness is represented by the  
letter-number v.
  (i) 10v (ii) 10 + v (iii) 2 × 10 × v
(iv) 2
10
 (v) 2
10
v (vi) 10
2
v
Some more examples of exponential notation:
4 × 4 × 4 = 4
3 
= 64.
(– 4) × (– 4) × (– 4) = (– 4)
3
= – 64.
Similarly,
a × a × a × b × b can be expressed as a
3
b
2
 (read as a cubed b squared).
a × a × b × b × b × b can be expressed as a
2
b
4
 (read as a squared b raised 
to the power 4).
Remember that 4 + 4 + 4 = 3 × 4 = 12, whereas 4 × 4 × 4 = 4
3
 = 64.
Express the number 32400 as a product of its prime factors 
and represent the prime factors in their exponential form.
32400 = 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3 × 3 × 3.
In exponential form, this would be
32400 = 2
4 
× 5
2 
× 3
4
.
What is (– 1)
5 
? Is it positive or negative? What about (– 1)
56 
? 
Is (– 2)
4
 = 16? Verify.
Figure it Out
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
32400 2
16200 2
8100 2
4050 2
2025 5
405 5
81 3
27 3
9 3
3 3
1
What is 0
2
, 0
5 
?
What is 0
n?
?
5
4
 is read as 
‘5 raised to the power 4’ or 
‘5 to the power 4’ or 
‘5 power 4’ or 
‘4th power of 5’
Chapter 2.indd   22 Chapter 2.indd   22 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Page 5


2
POWER PLAY
2.1 Experiencing the Power Play ...
An Impossible Venture!
Take a sheet of paper, as large a sheet as you can find. Fold it once. Fold 
it again, and again. 
How many times can you fold it over and over?
Estu says “I heard that a sheet of paper can’t be folded more than  
7 times”.
Roxie replies “What if we use a thinner paper, like a newspaper or a 
tissue paper?”
Try it with different types of paper and see what happens.
Say you can fold a sheet of paper as many times as you wish. What would 
its thickness be after 30 folds? Make a guess.
Let us find out how thick a sheet of paper will be after 46 folds. Assume 
that the thickness of the sheet is 0.001 cm.
If you can fold a paper 
46 times, it will be so 
thick that it can reach 
the Moon!
What! That’s crazy! 
Just 46 times!? You 
must have ignored 
several zeros 
after 46.
Well, why 
don’t you find 
out yourselves.
Chapter 2.indd   19 Chapter 2.indd   19 7/10/2025   3:29:53 PM 7/10/2025   3:29:53 PM
Ganita Prakash | Grade 8 
20
The following table lists the thickness after each fold. Observe that the 
thickness doubles after each fold.
Fold Thickness Fold Thickness Fold Thickness
1 0.002 cm 7 0.128 cm 13 8.192 cm
2 0.004 cm 8 0.256 cm 14 16.384 cm
3 0.008 cm 9 0.512 cm 15 32.768 cm
4 0.016 cm 10 1.024 cm 16 65.536 cm
5 0.032 cm 11 2.048 cm 17 ˜ 131 cm
6 0.064 cm 12 4.096 cm
(We use the sign ‘˜’ to indicate ‘approximately equal to’.)
After 10 folds, the thickness is just above 1 cm (1.024 cm).
After 17 folds, the thickness is about 131 cm (a little more than 4 feet).
Now, what do you think the thickness would be after 30 folds? 
45 folds? Make a guess.
Fill the table below.
Fold Thickness Fold Thickness Fold Thickness
18 ˜ 262 cm 21 24
19 ˜ 524 cm 22 25
20 ˜ 10.4 m 23 26
After 26 folds, the thickness is approximately 670 m. Burj Khalifa 
in Dubai, the tallest building in the world, is 830 m tall.
Fold Thickness Fold Thickness
27 ˜ 1.3 km 29
28 30
After 30 folds, the thickness of the paper is about 10.7 km, the 
typical height at which planes fly. The deepest point discovered in 
the oceans is the Mariana Trench, with a depth of 11 km.
Fold Thickness Fold Thickness Fold Thickness
31 36 41
32 37 42
33 38 43
34 39 44
35 40 45
Math 
Talk
Chapter 2.indd   20 Chapter 2.indd   20 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Power Play
21
It might be hard to digest the fact that after just 46 folds, the thickness 
is more than 7,00,000 km. This is the power of multiplicative growth, 
also called exponential growth. Let us analyse the growth.
We have seen that the thickness doubles after every fold.
Notice the change in thickness after two 
folds. By how much does it increase?
After any 3 folds, the thickness increases 8 
times (= 2 × 2 × 2). Check if that is true. Similarly, 
from any point, the thickness after 10 folds increases by 1024 times  
(= 2 multiplied by itself 10 times), as shown in the table below.
Fold Thickness Times increased by
0 to 10 1.024 cm – 0.001 cm 
= 1.023 cm
1.024 ÷ 0.001  
= 1024
10 to 20 10.485 m – 1.024 cm 
  ˜ 10.474 m
10.485 m ÷ 1.024 cm 
= 1024
20 to 30 10.737 km – 10.485 m
˜ 10.726 km
10.737 km ÷ 10.485 m
= 1024
30 to 40 10995 km – 10.737 km
 ˜ 10984.2 km
10995 km ÷ 
10.737 km = 1024
2.2 Exponential Notation and Operations
The initial thickness of the paper was 0.001 cm. 
Upon folding once, its thickness became 0.001 cm × 2 = 0.002 cm.
Folding it twice, its thickness became —
0.001 cm × 2 × 2 = 0.004 cm, or 0.001 cm × 2
2
 = 0.004 cm (in shorthand).
Upon folding it thrice, its thickness became —
0.001 cm × 2 × 2 × 2, or 0.001 cm × 2
3
 = 0.008 cm. 
When folded four times, its thickness became —
0.001 cm × 2 × 2 × 2 × 2, or 0.001 cm × 2
4
 = 0.016 cm.
Similarly, the expression for the thickness of the paper when folded 7 
times will be 0.001 cm × 2 × 2 × 2 × 2 × 2 × 2 × 2, or 0.001 cm × 2
7
 = 0.128 cm.
We have seen that square numbers can be expressed as n
2
 and cube 
numbers as n
3
.
n × n = n
2
 (read as ‘n squared’ or ‘n raised to the power 2’)
Fold 4 0.016 cm
Fold 5 0.032 cm
Fold 9 0.512 cm
Fold 10 1.024 cm
Fold 4 0.016 cm
Fold 6 0.064 cm
Chapter 2.indd   21 Chapter 2.indd   21 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Ganita Prakash | Grade 8 
22
n × n × n = n
3
 (read as ‘n cubed’ or ‘n raised to the power 3’)
n × n × n × n = n
4
 (read as ‘n raised to the power 4’ or ‘the 4th power of n’)
n × n × n × n × n × n × n = n
7
 (read as ‘n raised to the power 7’ or ‘the 7th 
power of n’) and so on.
In general, we write n
a
 to denote n multiplied by itself a times.
        5
4
 
= 5 × 5 × 5 × 5 = 625.
5
4
 is the exponential form of 625. Here, 4 is the 
exponent/power, and 5 is the base. Exponents of 
the form 5
n
 are called powers of 5: 5
1
, 5
2
, 5
3
, 5
4
, etc. 
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2
10
 = 1024. 
Remember the 1024 from earlier? There, it meant 
that after every 10 folds, the thickness increased 
1024 times.
Which expression describes the thickness of a sheet of paper after 
it is folded 10 times? The initial thickness is represented by the  
letter-number v.
  (i) 10v (ii) 10 + v (iii) 2 × 10 × v
(iv) 2
10
 (v) 2
10
v (vi) 10
2
v
Some more examples of exponential notation:
4 × 4 × 4 = 4
3 
= 64.
(– 4) × (– 4) × (– 4) = (– 4)
3
= – 64.
Similarly,
a × a × a × b × b can be expressed as a
3
b
2
 (read as a cubed b squared).
a × a × b × b × b × b can be expressed as a
2
b
4
 (read as a squared b raised 
to the power 4).
Remember that 4 + 4 + 4 = 3 × 4 = 12, whereas 4 × 4 × 4 = 4
3
 = 64.
Express the number 32400 as a product of its prime factors 
and represent the prime factors in their exponential form.
32400 = 2 × 2 × 2 × 2 × 5 × 5 × 3 × 3 × 3 × 3.
In exponential form, this would be
32400 = 2
4 
× 5
2 
× 3
4
.
What is (– 1)
5 
? Is it positive or negative? What about (– 1)
56 
? 
Is (– 2)
4
 = 16? Verify.
Figure it Out
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
32400 2
16200 2
8100 2
4050 2
2025 5
405 5
81 3
27 3
9 3
3 3
1
What is 0
2
, 0
5 
?
What is 0
n?
?
5
4
 is read as 
‘5 raised to the power 4’ or 
‘5 to the power 4’ or 
‘5 power 4’ or 
‘4th power of 5’
Chapter 2.indd   22 Chapter 2.indd   22 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM
Power Play
23
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 × 10
3
 (ii) 7
2
 × 2
3
 (iii) 3 × 4
4
 (iv) (– 3)
2
 × (– 5)
2
 (v) 3
2
 × 10
4
 (vi) (– 2)
5
 × (– 10)
6
The Stones that Shine ...
Three daughters with curious eyes,
Each got three baskets — a kingly prize.
Each basket had three silver keys,
Each opens three big rooms with ease.
Each room had tables — one, two, three,
With three bright necklaces on each, you see.
Each necklace had three diamonds so fine…
Can you count these stones that shine?
Hint: Find out the number of baskets and rooms. 
How many rooms were there altogether?
The information given can be visualised  as shown below.
From the diagram, the number of rooms is 3
4
. This can be computed 
by repeatedly multiplying 3 by itself,
3 × 3 = 9.
9 × 3 = 27.
27 × 3 = 81.
81 × 3 = 243.
How many diamonds were there in total? Can we find out by just one 
multiplication using the products above?
The number of diamonds is 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3
7
. 
King
daughters
baskets
keys
rooms
Chapter 2.indd   23 Chapter 2.indd   23 7/10/2025   3:29:55 PM 7/10/2025   3:29:55 PM