NCERT Solutions Class 7 Math Chapter 11 Exponents and Powers Exercise 11.1

(i) 26
Solution:  The above value can be written as,
= 2 × 2 × 2 × 2 × 2 × 2
= 64

(ii) 93
Solution: The above value can be written as,
= 9 × 9 × 9
= 729

(iii) 112
Solution: The above value can be written as,
= 11 × 11
= 121

(iv) 54
Solution: The above value can be written as,
= 5 × 5 × 5 × 5
= 625

(i) 6 × 6 × 6 × 6
Solution: The given question can be expressed in the exponential form as 64.

(ii) t × t
Solution: The given question can be expressed in the exponential form as t2.

(iii) b × b × b × b
Solution: The given question can be expressed in the exponential form as b4.

(iv) 5 × 5× 7 × 7 × 7
Solution: The given question can be expressed in the exponential form as 52 × 73.

(v) 2 × 2 × a × a
Solution: The given question can be expressed in the exponential form as 22 × a2.

(vi) a × a × a × c × c × c × c × d
Solution: The given question can be expressed in the exponential form as a3 × c4 × d.

(i) 512
Solution: The factors of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
So it can be expressed in the exponential form as 29.

(ii) 343
Solution: The factors of 343 = 7 × 7 × 7
So it can be expressed in the exponential form as 73.

(iii) 729
Solution: The factors of 729 = 3 × 3 × 3 × 3 × 3 × 3
So it can be expressed in the exponential form as 36.

(iv) 3125
Solution: The factors of 3125 = 5 × 5 × 5 × 5 × 5
So it can be expressed in the exponential form as 55.

(i) 43 or 34
Solution: The expansion of 43 = 4 × 4 × 4 = 64
The expansion of 34 = 3 × 3 × 3 × 3 = 81
Clearly,
64 < 81
So, 43 < 34
Hence 34 is the greater number.

(ii) 53 or 35
Solution: The expansion of 53 = 5 × 5 × 5 = 125
The expansion of 35 = 3 × 3 × 3 × 3 × 3= 243
Clearly,
125 < 243
So, 53 < 35
Hence 35 is the greater number.

(iii) 28 or 82
Solution: The expansion of 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
The expansion of 82 = 8 × 8= 64
Clearly,
256 > 64
So, 28 > 82
Hence 28 is the greater number.

(iv) 1002 or 2100
Solution: The expansion of 1002 = 100 × 100 = 10000
The expansion of 2100
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
Then,
2100 = 1024 × 1024 ×1024 × 1024 ×1024 × 1024 × 1024 × 1024 × 1024 × 1024 =
Clearly,
1002 < 2100
Hence 2100 is the greater number.

(v) 210 or 102
Solution: The expansion of 210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
The expansion of 102 = 10 × 10= 100
Clearly,
1024 > 100
So, 210 > 102
Hence 210 is the greater number.

(i) 648
Solution: Factors of 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3
= 23 × 34

(ii) 405
Solution: Factors of 405 = 3 × 3 × 3 × 3 × 5
= 34 × 5

(iii) 540
Solution: Factors of 540 = 2 × 2 × 3 × 3 × 3 × 5
= 22 × 33 × 5

(iv) 3,600
Solution: Factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 24 × 32 × 52

(i) 2 × 103
Solution: The above question can be written as,
= 2 × 10 × 10 × 10
= 2 × 1000
= 2000

(ii) 72 × 22
Solution: The above question can be written as,
= 7 × 7 × 2 × 2
= 49 × 4
= 196

(iii) 23 × 5
Solution: The above question can be written as,
= 2 × 2 × 2 × 5
= 8 × 5
= 40

(iv) 3 × 44
Solution: The above question can be written as,
= 3 × 4 × 4 × 4 × 4
= 3 × 256
= 768

(v) 0 × 102
Solution: The above question can be written as,
= 0 × 10 × 10
= 0 × 100
= 0

(vi) 52 × 33
Solution: The above question can be written as,
= 5 × 5 × 3 × 3 × 3
= 25 × 27
= 675

(vii) 24 × 32
Solution: The above question can be written as,
= 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9
= 144

(viii) 32 × 104
Solution: The above question can be written as,
= 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000
= 90000

(i) (– 4)3
Solution: The expansion of -43
= – 4 × – 4 × – 4
= – 64

(ii) (–3) × (–2)3
Solution: The expansion of (-3) × (-2)3
= – 3 × – 2 × – 2 × – 2
= – 3 × – 8
= 24

(iii) (–3)2 × (–5)2
Solution: The expansion of (-3)2 × (-5)2
= – 3 × – 3 × – 5 × – 5
= 9 × 25
= 225

(iv) (–2)3 × (–10)3
Solution: The expansion of (-2)3 × (-10)3
= – 2 × – 2 × – 2 × – 10 × – 10 × – 10
= – 8 × – 1000
= 8000

(i) 2.7 × 1012 ; 1.5 × 108
Solution: By observing the question
Comparing the exponents of base 10,
Clearly,
2.7 × 1012 > 1.5 × 108

(ii) 4 × 1014 ; 3 × 1017
Solution: By observing the question
Comparing the exponents of base 10,
Clearly,
4 × 1014 < 3 × 1017