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Number Line Prime Class 7 Solutions Chapter 6 Powers and Exponents
Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Number Line Prime Class 7 Math Book, Chapter 6, Powers and Exponents. Here students can easily find step by step solutions of all the problems for Powers and Exponents, Exercise 6A and 6B Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 6 solutions. Here in this post all the solutions are based on latest Syllabus.
Powers and Exponents Exercise 6A Solution :
Question no – (1)
Solution :
(a) (- 12)2
= (- 12) × (- 12)
= 144
(b) 53
= 5 × 53 × 5
= 125
(c) (- 10)3
= -10 × – 10 × – 10
= – 1000
(d) (- 6)2
= – 6 × – 6
= 36
Question no – (2)
Solution :
(a) 26 and 62
Given, 26
= 2 × 2 × 2 × 2 × 2 × 2
= 64
Given, 62
= 6 × 6
= 36
∴ 26 > 62
(b) 34 and 43
Given, 34
= 3 × 3 × 3 × 3
= 81,
Given, 43
= 4 × 4 × 4
= 64
∴ 43 > 34
(c) 54 and 63
Given, 54
= 5 × 5 × 5 × 5
= 625
Given, 63
= 6 × 6 × 6
= 261
∴ 54 > 63
(d) 73 and (- 6)4
Given, 73
= 7 × 7 × 7
= 343,
Given, (- 6)4
= (- 6) × (- 6) × (- 6) × (- 6)
= 1296
= (- 6)4 > 73
Question no – (3)
Solution :
(a) 63 × 22 – 23 + 33 × 23
= 216 × 4 – 8 + 27 × 8
= 864 – 8 + 216
= 1080 – 8
= 1072
(b) 23 ÷ 22 + 32 – 22
= 8 ÷ 4 + 9 – 4
= 2 + 9 – 4
= 11 – 4
= 7
(c) 42 ÷ 22 + 31 × 32 – 62
= 16 ÷ 4 + 3 × 9 – 36
= 4 + 27 – 36
= 31 – 36
= – 5
(d) 82 + 24 – 23
= 64 + 16 – 8
= 80 – 8
= 72
Question no – (4)
Solution :
(a) (- 6)7
= 7 is odd number
∴ Therefore it is a negative integer.
(b) (- 8)12
= 12 is even number,
∴ Therefore it is a positive integer.
(c)(- 2)315
= 315 is a odd number
∴ Therefore it is a negative integer.
(d) (- 543)31
= 31 is a odd number
∴ Therefore it is a negative number.
Question no – (5)
Solution :
(a) 2 × 2 × 2 × 2 × (- 4) × (- 4) × (- 4) × 5 × 5
= 24 × (- 4)3 × 52
(b) 3 × 3 × 3 ×(- 3) (- 3) × (- 3)
= 33 × (- 3)3
(c) (- 5) × (- 5) × (- 5) × (- 7) × (- 7) ×(- 7) × (- 11) × (- 11)
=(- 5)3 × (- 7)3 × (- 11)2
(d) (- 2) × (- 2) × ( – 2) × (- 3) × (- 3) × (- 3)
= (- 2)3 × (- 3)3
Question no – (6)
Solution :
(a) – 32
= – 2 × – 2 × – 2 × – 2 × – 2
= (- 2)5
(b) – 128
= – 2 × – 2 × – 2 × -2 × – 2 × – 2 × – 2
= (- 2)7
(c) 256
= – 2 × – 2 × – 2 × – 2 × – 2 × – 2 × – 2 × – 2
= (- 2)8
(d) 1024
= – 2 × – 2 × – 2 ×- 2 × – 2 × – 2 × – 2 × – 2 × – 2 × – 2
= (- 2)10
Question no – (7)
Solution :
(a) 250
= 5 × 5 × 5 × 2
= 53 × 21
(b) 500
= 5 × 5 × 5 × 2 × 2
= 53 × 22
(c) 4000
= 2 × 2 × 5 × 2 × 5 × 2 × 5 × 2
= 25 × 53
(d) 32000
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5
= 28 × 53
Question no – (8)
Solution :
(a) 24 × 30 + 8 × 5 + 4
= 720 + 40 + 4
= 764
= 2 × 2 × 191
= 22 × 191
(b) 80 × 20 × 50 × 20 × 60 × 10
= 80000 + 12000
= 92000
= 4 × 23 × 1000
= 22 × 231 × 103
(c) 72 – ( – 4)2 + 52 × 32 – ( – 4)0 × 23 + 52 × 2
= 72 – 16 + 25 × 9 – 1 × 23 + 25 × 2
=72 – 16 + 225 – 23 + 50
= 347 – 39
= 308
= 2 × 2 × 7 × 11
= 22 × 71 × 111
(d) (- 3)3 + (- 4)2 + 5 × 33 + (- 1)2 × 4
= – 27 + 16 + 5 × 27 + 1 × 4
= – 27 + 16 + 135 + 4
= – 27 + 155
= 128
= 2 × 2 × 2 × 2 × 2 × 2 × 2
= 27
Powers and Exponents Exercise 6B Solution :
Question no – (1)
Solution :
(a) 26 × 24 ÷ 28
= 26 × 2(4 – 8)
= 26 × 2(- 4)
= 2(6-4)
= 22
= 4
(b) 32 × 32 ÷ 36
= 32 × 3(2-6)
= 32 × 3-4
= 3(2-4)
= 3-2
= 1/32
= 1/9
(c) 42 × 4
= 4(2+1)
= 43
= 64
(d) 24 × 25 × 20
= 2(4 + 5 + 0)
= 29
= 512
Question no – (2)
Solution :
(a) [(23)8]4
= [224]4
= 296
(b) [(52)4]4/(84)8
= (52)4 × 44/816
= 58 × 44/816
(c) (54)8 ×5-6
= 540×5– 6
=5(40 – 6)
=534
(d) 38 × 39 ÷ 350
= 38 ÷ 3(9 – 50)
= 38 ÷ 3– 41
= 3(8 – 41)
= 3– 33
= 1/333
Question no – (3)
Solution :
(a) (3-3)2 ÷ 1/81
= 3– 6 ÷ 1/34
= 3– 6 ÷ 3-4
= 3(- 6 + 4)
= 3– 2
= 1/32
= 1/9
(b) 256 × 1/26 × 2-4
= 28 × 1/26 × 2-4
= 2(8 – 6) × 2-4
= 22 × 2– 4
= 2(2 – 4)
= 1/22
= 1/4
(c) (18)5 × (32)– 4 × (2 -4)2
= (9 × 2)5 × 3-8 × 2-8
= (32)5 × 52 × 3– 8 × 2– 8
= 3(10 – 8) × 2(5 – 8)
= 32/23
= 9/8
(d) (216)2 ÷ (73) × (3)9 × (2-2)3
= (36 × 76) ÷ 79 × 39 × 2 – 6
= 312 × 712 ÷ 79 × 39 × 2– 6
= 312 × 7(12 – 9) × 39 × 2– 6
= 3(12 + 9) × 73 × 2– 6
= 321 × 73/26
Question no – (4)
Solution :
(a) (- 6)8 × (- 5)– 5 ÷ (- 5)– 10
= (- 5)8 × (- 5)(- 5 + 10)
= (- 5)8 × (- 5)5
= (- 5)8 + 5
= (- 5)13
(b) 28 × (23)2 ÷ (22)5
= 28 × 26 ÷ 210
= 28 × 2(6-10)
=28× 2-4
= 2(8 – 4)
= 24
(c) 911 ÷ (95)2 × (93)5 × 94
= 9(11-10) × 915 × 94
= 91 × 915 × 94
= 9(1 + 15 + 4)
= 920
(d) (-15-3)4 × (38)2 × (54)4
(15)-12 × 316 × 516
= 3-12 × 5-12 × 316 × 516
=3-12+16) × 5(12+16)
= 34 × 54
= (15)4
Question no – (5)
Solution :
(a) (x3yz4)12
= x36y12z48
(b) (x3y2)5 ÷ 1/x5y5
= (x3y2)5 ÷ 1/x-5y-5
= x15y10 ÷ x-5y-5
= x15y10 ÷ x-5y-5
= x(15 + 5)y(10 + 5)
= x20y15
(c) p-5q-6 ÷ 1/(p-2q-2)2
= p-5q-6 ÷ p-4q-4
= p(-5-4)q(-6-4)
= 1/p9q10
(d) (a3b3)8 ÷ a8b8 × a16b16
= (a3b5/ab)8 × a16b16
= (a2b2)8 × a16b16
= a16b32 × a16b16
= a32b48
Question no – (6)
Solution :
(a) 1/p-2q2r-5
= p2r5/q2
(b) (x-2y3)-6
= (1/x-2y3)6
= (x2/y3)6
= x12/y18
(c) x-2+ y-2z-2
= 1/x2+1/y2z2
(d) a4b4c2/a4b5c
= c4-1/b4-5
= c3/b1
Question no – (7)
Solution :
According to the above question we know,
x = 2, y = 3
(a) (2x)4
= (2 × 2)4
= 44
= 256
(b) (- 3xy)2
= (-3 × 2 × 3)2
= 81 × 4
= 324
(c) xx+y
= 22+5
= 25
= 32
(d) 5x + 2y
= 5 × 2 + 2 × 3
= 10 + 6
= 16
(e) -7xy
= -723
= 7 × 8
= – 56
(f) xy + yx
= 23 + 32
= 8 + 9
= 17
Question no – (8)
Solution :
(a) {(9/16)-2× (-96)2}-1
= (9/16)2 × (-96)-2
= 92/162 × 1/(-96)2
= 92/162 × 1/162 × 62
= 81/2359296
(b) [{(23+ 30– 13) × (5/9)3} ÷ (5/9)5]
= [{(8 + 1 – 1) × 53/93} ÷ 55/65]
= [8 × 53/93 ÷ 55/65]
= [8 × 5(3-5)/9(3-5)]
= 8 × 5-2/9-2
= 8 × 92/52
= 8 × 81/25
= 648/25
Question no – (9)
Solution :
(a) 7,20,00,00,000
= 7.2 × 109
(b) 23,45,00,000
= 2.345 × 108
(c) 6,99,99,99,990
= 6.99999999 × 109
(d) 76/10,000
= 7.6 × 10-5
Question no – (10)
Solution :
(a) 9.018 × 105
= 90800
(b) 8.9 × 10-4
= 89/100000
Next Chapter Solution :
