NCERT Solutions Class 7 Mathematics
Chapter – 13 (Exponents and Powers)
The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 13 Exponents and Powers Exercise 13.1 has been provided here to help the students in solving the questions from this exercise.
Chapter : 13 Exponents and Powers
Exercise – 13.1
1. Find the value of:
(i) 26
(ii) 93
(iii) 112
(iv) 54
Solution –
(i) 26
= 2 × 2 × 2 × 2 × 2 × 2
= 64
(ii) 93
= 9 × 9 × 9
= 729
(iii) 112
= 11 × 11
= 121
(iv) 54
= 5 × 5 × 5 × 5
= 625
2. Express the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(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
Solution –
(i) 6 × 6 × 6 × 6
The given question can be expressed in the exponential form as 64.
(ii) t × t
The given question can be expressed in the exponential form as t2.
(iii) b × b × b × b
The given question can be expressed in the exponential form as b4.
(iv) 5 × 5× 7 × 7 × 7
The given question can be expressed in the exponential form as 52 × 73.
(v) 2 × 2 × a × a
The given question can be expressed in the exponential form as 22 × a2.
(vi) a × a × a × c × c × c × c × d
The given question can be expressed in the exponential form as a3 × c4 × d.
3. Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125
Solution –
(i) 512
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
The factors of 343 = 7 × 7 × 7
So it can be expressed in the exponential form as 73.
(iii) 729
The factors of 729 = 3 × 3 × 3 × 3 × 3 × 3
So it can be expressed in the exponential form as 36.
(iv) 3125
The factors of 3125 = 5 × 5 × 5 × 5 × 5
So it can be expressed in the exponential form as 55.
4. Identify the greater number, wherever possible, in each of the following?
(i) 43 or 34
(ii) 53 or 35
(iii) 28 or 82
(iv) 1002 or 2100
(v) 210 or 102
Solution –
(i) 43 or 34
The expansion of 43 = 4 × 4 × 4 = 64
The expansion of 34 = 3 × 3 × 3 × 3 = 81
Clearly, 64 < 81
∴ 34 is greater than 43.
(ii) 53 or 35
The expansion of 53 = 5 × 5 × 5 = 125
The expansion of 35 = 3 × 3 × 3 × 3 × 3= 243
Clearly, 125 < 243
∴ 35 is greater than 53.
(iii) 28 or 82
The expansion of 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
The expansion of 82 = 8 × 8= 64
Clearly, 256 > 64
∴ 28 is greater than 28.
(iv) 1002 or 2100
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 = 1267650600228229401496703205376
Clearly, 1002 < 2100
∴ 2100 is greater than 1002.
(v) 210 or 102
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
∴ 210 is greater than 102.
5. Express each of the following as product of powers of their prime factors:
(i) 648
(ii) 405
(iii) 540
(iv) 3600
Solution –
(i)
Factors of 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3
= 23 × 34
(ii) 405
Factors of 405 = 3 × 3 × 3 × 3 × 5
= 34 × 5
(iii) 540
Factors of 540 = 2 × 2 × 3 × 3 × 3 × 5
= 22 × 33 × 5
(iv) 3,600
Factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
= 24 × 32 × 52
6. Simplify:
(i) 2 × 103
(ii) 72 × 22
(iii) 23 × 5
(iv) 3 × 44
(v) 0 × 102
(vi) 52 × 33
(vii) 24 × 32
(viii) 32 × 104
Solution –
(i) 2 × 103
The above question can be written as,
= 2 × 10 × 10 × 10
= 2 × 1000
= 2000
(ii) 72 × 22
The above question can be written as,
= 7 × 7 × 2 × 2
= 49 × 4
= 196
(iii) 23 × 5
The above question can be written as,
= 2 × 2 × 2 × 5
= 8 × 5
= 40
(iv) 3 × 44
The above question can be written as,
= 3 × 4 × 4 × 4 × 4
= 3 × 256
= 768
(v) 0 × 102
The above question can be written as,
= 0 × 10 × 10
= 0 × 100
= 0
(vi) 52 × 33
The above question can be written as,
= 5 × 5 × 3 × 3 × 3
= 25 × 27
= 675
(vii) 24 × 32
The above question can be written as,
= 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9
= 144
(viii) 32 × 104
The above question can be written as,
= 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000
= 90000
7. Simplify:
(i) (– 4)3
(ii) (-3) × (-2)3
(iii) (-3)2 × (-5)2
(iv) (-2)3 × (-10)3
Solution –
(i) (– 4)3
The expansion of -43
= – 4 × – 4 × – 4
= – 64
(ii) (–3) × (–2)3
The expansion of (-3) × (-2)3
= – 3 × – 2 × – 2 × – 2
= – 3 × – 8
= 24
(iii) (–3)2 × (–5)2
The expansion of (-3)2 × (-5)2
= – 3 × – 3 × – 5 × – 5
= 9 × 25
= 225
(iv) (–2)3 × (–10)3
The expansion of (-2)3 × (-10)3
= – 2 × – 2 × – 2 × – 10 × – 10 × – 10
= – 8 × – 1000
= 8000
8. Compare the following numbers:
(i) 2.7 × 1012 ; 1.5 × 108
(ii) 4 × 1014; 3 × 1014
Solution –
(i) 2.7 × 1012 ; 1.5 × 108
Here, 1012 > 108
∴ 2.7 × 1012> 1.5 × 108
(ii) 4 × 1014 ; 3 × 1017
Here, 1017 > 1014
∴ 4 × 1014 < 3 × 1017