NCERT Solutions for Class 8 Maths – Ganita Prakash
Chapter 2: Power Play
Exercise 2.1
1. Express the following in exponential form:
(i) 6 × 6 × 6 × 6
Here, 6 is multiplied 4 times.
= 64
(ii) y × y
Here, y is multiplied 2 times.
= y2
(iii) b × b × b × b
Here, b is multiplied 4 times.
= b4
(iv) 5 × 5 × 7 × 7 × 7
Here, 5 is multiplied 2 times and 7 is multiplied 3 times.
= 52 × 73
(v) 2 × 2 × a × a
Here, 2 is multiplied 2 times and a is multiplied 2 times.
= 22 × a2
(vi) a × a × a × c × c × c × c × d
Here, a is multiplied 3 times, c is multiplied 4 times and d comes 1 time.
= a3 × c4 × d
2. Express each of the following as a product of powers of their prime factors in exponential form.
(i) 648
648 = 2 × 324
= 2 × 2 × 162
= 2 × 2 × 2 × 81
= 23 × 81
= 23 × 34
Therefore, 648 = 23 × 34
(ii) 405
405 = 5 × 81
= 5 × 34
Therefore, 405 = 34 × 5
(iii) 540
540 = 54 × 10
= (2 × 33) × (2 × 5)
= 22 × 33 × 5
Therefore, 540 = 22 × 33 × 5
(iv) 3600
3600 = 36 × 100
= (22 × 32) × (22 × 52)
= 24 × 32 × 52
Therefore, 3600 = 24 × 32 × 52
3. Write the numerical value of each of the following:
(i) 2 × 103
= 2 × 1000
= 2000
Answer: 2000
(ii) 72 × 23
= 49 × 8
= 392
Answer: 392
(iii) 3 × 44
44 = 256
So, 3 × 44 = 3 × 256 = 768
Answer: 768
(iv) (−3)2 × (−5)2
(−3)2 = 9
(−5)2 = 25
So, 9 × 25 = 225
Answer: 225
(v) 32 × 104
32 = 9
104 = 10000
So, 9 × 10000 = 90000
Answer: 90000
(vi) (−2)5 × (−10)6
(−2)5 = −32
(−10)6 = 1000000
So, −32 × 1000000 = −32000000
Answer: −32000000