## NCERT Solutions for class 7 Maths Chapter 13: Exponents and Powers## Exercise 13.1
2 × 2 × 2 × 2 × 2 × 2 = 64
9 × 9 × 9 = 81 × 9 = 729
11 × 11 = 121
5 × 5 × 5 × 5 = 25 × 25 = 625
Hence, it can be represented as: 6
Hence, it can be represented as: t
Hence, it can be represented as: b
The number 5 is repeated two times and the number 7 is repeated three times. Hence, it can be represented as: 5
The number 2 is repeated two times and the variable 'a' is also repeated two times. Hence, it can be represented as: 2
The variable 'a' is repeated three times, variable 'c' four times, and the variable 'd 'one time. Hence, it can be represented as: a
= 2 × 256 = 2 × 2 × 128 = 2 × 2 × 2 × 64 = 2 × 2 × 2 × 2 × 32 = 2 × 2 × 2 × 2 × 2 × 16 = 2 × 2 × 2 × 2 × 2 × 2 × 8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 4 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 The number 2 is repeated nine times. Hence, it can be written as: = 2
= 7 × 49 = 7 × 7 × 7 The number 7 is repeated three times. Hence, it can be written as: = 7
= 3 × 243 = 3 × 3 × 81 = 3 × 3 × 3 × 27 = 3 × 3 × 3 × 3 × 9 = 3 × 3 × 3 × 3 × 3 × 3 The number 3 is repeated six times. Hence, it can be written as: = 3
= 5 × 625 = 5 × 5 × 125 = 5 × 5 × 5 × 25 = 5 × 5 × 5 × 5 × 5 The number 5 is repeated five times. Hence, it can be written as: = 5
4 × 4 × 4 = 16 × 4 = 64 3 3 × 3 × 3 × 3 = 9 × 3 × 3 = 27 × 3 = 81 81 > 64 Hence, 3
5 × 5 × 5 = 25 × 5 = 125 3 3 × 3 × 3 × 3 × 3 = 9 × 3 × 3 × 3 = 27 × 3 × 3 = 81× 3 = 243 243 > 125 Hence, 3
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 16 × 16 = 256 8 8 × 8 = 64 256 > 64 Hence, 2
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 16 × 16 × 4 = 1024 10 10 × 10 = 100 1024 > 100 Hence, 2
= 2 × 324 = 2 × 2 × 162 = 2 × 2 × 2 × 81 = 2 × 2 × 2 × 3 × 27 = 2 × 2 × 2 × 3 × 3 × 9 = 2 × 2 × 2 × 3 × 3 × 3 × 3 The number 2 is repeated three times and the number 3 is repeated four times. Hence, it can be written as: 2
= 5× 81 = 5 × 3 × 27 = 5 × 3 × 3 × 9 = 5 × 3 × 3 × 3 × 3 The number 5 is repeated one time and the number 3 is repeated four times. Hence, it can be written as: 5 = 5× 3
= 2 × 270 = 2 × 27 × 10 = 2 × 3 × 3 × 3 × 2 × 5 = 2
= 60 × 60 = 3 × 2 × 2 × 5 × 3 × 2 × 2 × 5 The number 3 is repeated two times, the number 2 four times, and the number 5 two times. Hence, the expression can be written as: 2
The number 10 is repeated three times. = 2 × 10 × 10 × 10 = 2 × 1000 = 2000
= 7 × 7 × 2 × 2 = 49 × 4 = 196
= 2 × 2 × 2 × 5 = 8 × 5 = 40
= 3 × 4 × 4 × 4 × 4 = 3 × 16 × 16 = 3 × 256 = 768
= 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675
= 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144
= 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000
= (- 4) × (- 4) × (- 4) = 16 × (- 4) = - 64
(-3) × (-2) =(-3) × (-2) × (-2) × (-2) = 6 × (-2) × (-2) = -12 × (-2) = 24
(-3) = (-3) × (-3) × (-5) × (-5) = 9 × (-5) × (-5) = (-45) × (-5) = 225
(-2) = (-2) × (-2) × (-2) × (-10) × (-10) × (-10) = (-8) × (-1000) = 8000
2.7 × 10 1.5 × 10 Hence, 2.7 × 10 2.7 × 10
3 × 10 Or 4 × 10 ## Exercise 13.2
3 3
6 6
a a
7 7
(5 (5 In the case of division, the exponents are subtracted if the base of numbers is the same. 5 5
2 2
a a
(3 (3
In the case of division, the exponents are subtracted if the base of numbers is the same. = 2 = 2 In the case of multiplication, the exponents are added if the base of numbers is the same. = 2 = 2 (x) 8
In the case of division, the exponents are subtracted if the base of numbers is the same. = 8
4 can be written as: 2 × 2 = 2 32 can be written as: 2 × 2 × 2 × 2 × 2 = 2 Substituting the value of 4 and 32 in the expression, (2 In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same. = (2 = (2 = (2
The exponents in the case of double brackets are multiplied. (5 (5 ((5 (5 In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same. = (5 = (5 = 5 = 5
25 can be written as: 5 × 5 = 5 Substituting the value of 25 in the expression, (5 The exponents in the case of double brackets are multiplied. (5 (5 In the case of division, the exponents are subtracted if the base of numbers is the same. 5 = 5 = 5
21 can be written as: 3 × 7 Substituting the value of 21 in the expression, (3 × 7 In the case of division, the exponents are subtracted, and added in the case of multiplication if the base of numbers is the same. (3 = (3 = (1× 7 = (7× 11
In the case of multiplication, the exponents are added if the base of numbers is the same. = 3 = 3 In the case of division, the exponents are subtracted if the base of numbers is the same. = 3 = 3 = 1
2 3 4 Substituting the value in the expression, we get: 2 = 1 + 1 + 1 = 3
2 3 4 Substituting the value in the expression, we get: 2 = 1 × 1 × 1 = 1
2 3 5 Substituting the value in the expression, we get: (3 = (1 + 1) × 1 = 2 × 1 = 2
4 can be written as: 2 × 2 = 2 Substituting the value of 4 in the expression, (2 (2 (2 = (2 In the case of division, the exponents are subtracted if the base of numbers is the same. = (2 = (2 = (2a)
= (a = (a = a = a
4 can be written as: 2 × 2 = 2 Substituting the value of 4 in the expression, ((2 (2 (2 (2 = (2 = (2 = a
= 2 In the case of multiplication, the exponents are added if the base of numbers is the same. = 2 = 2
The expression can be written as: 10 × 10 = 10 In the case of multiplication, the exponents are added if the base of numbers is the same. = 10 = 10 Thus, the correct expression is:
100 (10 = 10 = 10 Thus, 100
2 × 2 × 2 = 8 5 5 × 5 = 25 8 < 25 Thus, 2
2 × 2 × 2 = 8 3 3 × 3 = 9 8 + 9 = 17 Thus, the given statement is incorrect. 6 6
3 1000 Hence, the given expression is true. 1 = 1 3
= 2 × 54 = 2 × 2 × 27 = 2 × 2 × 3 × 9 = 2 × 2 × 3 × 3 × 3 = 2 192 can be written as: = 2 × 96 = 2 × 2 × 48 = 2 × 2 × 2 × 24 = 2 × 2 × 2 × 2 × 12 = 2 × 2 × 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2 108 × 192 = (2 In the case of multiplication, the exponents are added if the base of numbers is the same. 108 × 192 = (2 108 × 192 =
= 27 × 10 = 3 × 3 × 3 × 5 × 2 = 3
= 3 × 243 = 3 × 3 × 81 = 3 × 3 × 3 × 27 = 3 × 3 × 3 × 3 × 9 = 3 × 3 × 3 × 3 × 3 × 3 = 3 64 can be written as: = 2 × 32 = 2 × 2 × 16 = 2 × 2 × 2 × 8 = 2 × 2 × 2 × 2 × 4 = 2 × 2 × 2 × 2 × 2 × 2 = 2 729 × 64 = 3
= 2 × 384 = 2 × 2 × 192 = 2 × 2 × 2 × 96 = 2 × 2 × 2 × 2 × 48 = 2 × 2 × 2 × 2 × 2 × 24 = 2 × 2 × 2 × 2 × 2 × 2 × 12 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2
8 can be written as: 2 × 2 × 2= 2 Substituting the value of 8 in the expression, ((2 = (2 = (2 =(2 = 2 × 49 = 98
25 can be written as: 5 × 5 = 5 10 2 Substituting the value of 25 and 10 (5 = (5 =(5 = 5t
25 can be written as: 5 × 5 = 5 10 2 6 2 Substituting the value of 25, 10 (3 = (3 = (3 = (1 × 1 × 1) = 1 ## Exercise 13.3
279404 = 200000 + 70000 + 9000 + 400 + 4
= 2 × 10
3006194 = 3000000 + 6000 + 100 + 90 + 4
= 3 × 10
2806196 = 2000000 + 800000 + 6000 + 100 + 90 + 6
= 2 × 10
120719 = 100000 + 20000 + 700 + 10 + 9
1 × 10 20068 20068 = 20000 + 60 + 8
2 × 10
= 86045
= 405302
30705
900230
5 × 10
7 × 10
31865 × 10 Let's convert the number into the single decimal number. 3.1865 × 10 = 3.1865 × 10
3.90878 × 10
3.90878 × 10
384 × 10 = 3.84 × 10 = 3.84 × 10
3 × 10
1.2756 × 10
1.4 × 10
10 Or 1 × 10
1.2 × 10
3 × 10
6.023 × 10
1.353 × 10
1.027 × 10 Next TopicNCERT Solutions for class 8 Maths |