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Joy of Mathematics Class 8 Solutions Chapter 3 Exponents
Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of Joy of Mathematics Class 8 Book, Chapter 3 Exponents. Here students can easily find step by step solutions of all the problems for Exponents. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here students will find solutions for Exercise 3.1 and 3.2
Exponents Exercise 3.1 Solution
Question no – (1)
Solution :
(a) 5 × 5 × 5 × 5 × 5
= 55
(b) 7 × 7 × 7 × 7
= 74
(c) (-2/5) × (-2/5) × (-2/5) × (-2/5)
= (-2/5)4
(d) a × a × b × b × b × c × c × c × c
= a2 × b3 × c4
(e) (- 2) × (- 2) × a × a × a × a
= (- 2)2 × a4
(f) 2/3 × 2/3 × 2/3 × (- x) × (- x) × (- x) × (- x)
= (2/3)3 × (-x)4
Question no – (2)
Solution :
(a) Given, 34
= Here, exponents = 4,
base = 3
(b) Given, (-1)5
= Here, exponents =5
base = -1
(c) Given, (0.3)7
= Here, exponents = 7
base = 0.3
(d) Given, (2/11)6
Here, exponents = 6
base = 2/11
(e) Given, (10)4
Here, exponents =4
base = 10
(f) Given, (- 1)10
Here, exponents =10
base = – 1
Question no – (3)
Solution :
(a) Given, 32
= 3 × 3
= 9
(b) Given, 92
= 9 × 9
= 81
(c) Given, (12/11)3
= 12 × 12 × 12 / 11 × 11 × 11
= 1728/1331
(d) Given, (- 1/4)3
= – 1/4 × (- 1/4) × (- 1/4)
= – 1/64
(e) Given, (3/5)3
= 3/5 × 3/5 × 3/5
= 27/125
(f) Given, (-1)21
= -1
(g) Given, (-1)100
= 1
(h) Given, (0.1)5
= 0.1 × 0.1 × 0.1 × 0.1 × 0.1
= 0.00001
Question no – (4)
Solution :
(a) Given, (- 2)3
= – 2 × – 2 × – 2
= – 8
(b) Given, (- 3)3
= – 3 × (- 3) × (- 3)
= – 27
(c) Given, (- 4)4
= – 4 × (- 4) × (- 4) × (- 4)
= 258
(d) Given, 73
= 7 × 7 × 7
= 343
(e) Given, (-1/4)3
= (- 1/4) × (- 1/4) × (- 1/4)
= – 1/64
(f) Given, (5/3)2
= 5/3 × 5/3
= 25/9
(g) Given, (3/5)3
= 3/5 × 3/5 × 3/5
= 27/125
(h) Given, (5/7)4
= 5/7 × 5/7 × 5/7 × 5/7
= 625/2401
Question no – (5)
Solution :
(a) Given, 27/125
= 3 × 3 × 3/5 × 5 × 5
= 3/5 × 3/5 × 3/5
= (3/5)3
(b) Given, – 64/729
= – 4 × 4 × 4/9 × 9 × 9
= (- 4/9)3
(c) Given, 16/49
= 2 × 2 × 2 × 2/7 × 7
= 4/7 × 4/7
= (4/7)2
(d) Given, 36/64
= 6 × 6/8 × 8
= (6/8)2
(e) Given, 1/10000
= 1/100 × 100
= (1/100)2
(f) Given, – 8/27
= – 2 × 2 × 2/3 × 3 × 3
= – 2/3 × 2/3 × 2/3
= (- 2/3)3
(g) Given, 1331/2197
= 11 × 11 × 11/13 × 13 × 13
= 11/13 × 11/13 × 11/13
= (11/13)3
(h) Given, – 343/1024
= – 7 × 7 × 7 /32 × 32
= – (7)3/(32)2
Question no – (6)
Solution :
(a) Given, 500
= 2 × 250
= 2 × 5 × 50
= 2 × 5 × 5 × 10
= 2 × 5 × 5 × 5 × 2
= 22 × 53
(b) Given, 675
= 5 × 5 × 3 × 3 × 3
= 52 × 33
(c) Given, 1372
= 2 × 2 × 7 × 7 × 7
= 22 × 73
(d) Given, 6125
= 5 × 5 × 5 × 7 × 7
= 53 × 72
(e) Given, 6000
= 3 × 5 × 5 × 5
= 31 × 53 × 24
(f) Given, 90000
= 3 × 3 × 5 × 5 × 5 × 5 × 2 × 2 × 2 × 2
= 32 × 54 × 24
(g) Given, 10000
= 5 × 5 × 5 × 5 × 2 × 2 × 2 × 2
= 54 × 24
(h) Given, – 432
= – 2 × 2 × 2 × 2 × 3 × 3 × 3
= – 24 × 33
Question no – (7)
Solution :
(a) (-2)3 or (-3)2
= – 8 or -27
∴ (-2)3 > (- 3)2
(b) 25 or 52
= 2 × 2 × 2 × 2 × 2 or 5 × 5
= 32 or 25
∴ 25 > 52
(c) 36 or 63
= 3 × 3 × 3 × 3 × 3 × 3 or 6 × 6 × 6
= 729 or 216
∴ 36 > 63
(d) 26 or 62
= 2 × 2 × 2 × 2 × 2 × 2 or 6 × 6
= 64 or 36
∴ 26 > 62
Question no – (8)
Solution :
(a) p3 + q3
= (- 2)3 + (4)3
= – 8 + 64
= 56
(b) (4p + q)2
= (4 × (-2) + 4)2
= (- 8 + 4)2
= (- 4)2
= 16
(c) (4p)2
= (4 × (-2)2
= (-8)2
= 64
(d) p3 q2
= (-2)3 × (4)2
= – 8 × 16
= – 124
Question no – (9)
Solution :
Here, x = 3, y = – 2
(a) Given, (x – y)3
= (3 + 2)3
= (5)3
= 125
(b) Given, (2x- 3y)2
= (2 × 3 – 3 × (- 2))2
= (6 + 6)2
= (12)2
= 144
(c) Given, (x – y)x
= (3 + 2)3
= (5)3
= 125
(d) Given, (x/y + y/x)x
= (2/-3 + – 2/3)3
= (- 2/3 – 2/3)3
= (- 2 – 2/3)3
= (- 4/3)3
= – 4/3 × 4/3 × 4/3
= – 64/27
Question no – (10)
Solution :
Here, x = 3, y = 2, z = 1
Then,
(a) xy + yz+ zx
= 32 + 21 + 13
= 9 + 2 + 1
= 12
(b) (xy) (yz) (zx)
= (32) (21) (13)
= 9 × 2 × 1
= 18
(c) (x)y+z + (y)z+x + (z)x+y
= (3)2+1 + (2)1+3 + (1)3+2
= 33 + 24 + 15
= 27 + 16 + 1
= 44
Exponents Exercise 3.2 Solution
Question no – (1)
Solution :
(a) 23 × 24 × 25
= 23+4+(-5)
= 23+4-5
= 27-5
= 22
(b) (- 3)4 × (- 3)5 × (- 3)2
= (- 3)4+5+2
= (- 3)11
(c) a5 × a7
= a5+7
= a12
(d) (74)5
= 74×5
= 720
(e) (52)-4
= 52×(-4)
= 5-8
(f) (212 ÷ 27) × 9-5
= 212-7 × 9-5
= 25 × 1/95
= (2/9)5
(g) (8/5)-6 × (- 5/8)-2
= (8/5)-6 × (-8/5)2
= (8/5)6 × (-1)2 × (8/5)2
= (8/5)6+2
= (8/5)8
(h) (32)3 ÷ (63)2
= 36 ÷ 66
= (3/6)6
= (1/2)6
(i) (43)4 ÷ (42)6
= 412 ÷ 412
= (4/4)12
= (1)12
= 12
Question no – (2)
Solution :
(a) 25 × 35
= (2/3)5
(b) 30 × 40 × 50
= 1 × 1 × 1 [∵ 40 = 1, 30 = 1, 50 = 1]
= (1)1
(c) 60 × 23 × 33
= 1 × 23 × 1/33
= (2/3)3
(d) (20 + 40) ÷ 2
= (1 + 1) ÷ 2 [∵ 20 = 40 = 1]
= 2/2
= 1
(e) 2-4 × 93 × 4
= 1/24 × 93 × 22
= 22/24 × 93
= 93/24-2
= 93/22
(f) (30 + 60) ÷ 90
= (1 + 1) ÷ 1 [∵ 30 = 60 – 90 = 1]
= 2/1
= 2
(g) 25 × 2-4 ÷ 28
= 25-4 ÷ 28
= 21-8
= 2-7
(h) (-7)3 ÷ (-7)6 × (-7)5
= (-7)3-6 × (-7)5
= (-7)-3 × (-7)5
= (-7)-3+5
= (-7)2
Question no – (3)
Solution :
(a) 2-6 – 50 × 25
= 1/26 – 1 × 32
= 1/64 – 32
= 1 – 2048/64
= – 2047/64
(b) 8 × 2-3 – 26 + 50
= 8/8 – 64 + 1
= 1 – 64 + 1
= 2 – 64
= – 62
(c) 2 × 35 – 6 × 64
= 2 × 243 – (6)5
= 486 – 7776
= – 7290
(d) 12 + 22 + 72 + 24
= 1 + 4 + 49 + 16
= 21 + 49
= 70
Question no – (4)
Solution :
(a) 23 × 32 = 65
L.H.S. 23 × 32
= 8 × 9
= 72 ≠ R.H.S (False)
(b) L.H.S. 26 × 30 × 50
= 26 × 1 × 1
= 26 ≠ 30 (False)
(c) L.H.S. 20 + 70 + 50
= 1 + 1 + 1
= 3 = R.H.S. (True)
(d) L.H.S. 20 × 31 × 52
= 1 ∴ 3 × 25
= 75 ≠ R.H.S. = 303 (False)
(e) L.H.S. 32 = 9
R.H.S. 43 = 64
L.H.S. ≠ R.H.S. (False)
(f) L.H.S. 83 × 53
= 512 × 125
= 674000
R.H.S. (10)3 = 10 × 10 × 10
∴ L.H.S. ≠ R.H.S. (False)
(g) L.H.S. a0 + b0 /a0 × b0
= 1 + 1/1 × 1
= 2/1 = R.H.S (True)
(h) L.H.S. 5 × 57 = 51+7
= 58
R.H.S. (25)7
= (52)7
= 514
L.H.S. ≠ R.H.S (False)
Question no – (5)
Solution :
(a) In (-2)5, – 2 is called base and 5 is called exponential.
(b) For all values of n, (1)n equals 1.
(c) The value of (- 5)0 equals 1.
(d) The value of (25)0 equals 1.
Question no – (6)
Solution :
Given, a = – 2, b = – 3
then, 2a3 + (b3)2 – a2
= 2(-3)3 + (-33)2 – (-2)2
= 2(-27) + (-27)2 – 4
= – 54 + 729 – 4
= 729 + 58
= 671
Question no – (7)
Solution :
(a) 34 × (-5)-4/9 × (52)3
= 34 × (-1)4/32 × (5)4 (5)6
= 34-2/54+6
= 32/510
= 9/510
(b) (-5)2 × 6-2 × 32/36 × (- 5)4
= (-5)2 × 32/(6)2 62 × (-5)4
= 32/(-5)4-2 (6)2+2
= 32/(-5)2 64
= (3/5)2 1/64
= 9/25 × 1296
= 9/32400
= 1/3600
(c) 30 + (52)3 – 62/(32)3 × 52
= 1 + 56 – 36/36 × 25
= 1 + 15625 – 36/729 × 25
= 1590/18225
Question no – (8)
Solution :
(a) 26 × 32 × (-5)-2/9 × 5-4
= 26 × 32/32 × (-5)2 × (5)-4
= 26 32-2/(-5)2-4
= 26 30/-5-2
= 26 × 1(- 5)2
= 26 × (5)2
(b) (63)2 × (- 32)2/18 × 33
= (6)6 × (-3)4/3 × 6 × 33
= (6)6-1 × (3)4-4
= 65 × 30
= 65 × 1
= 65
(c) 20 × (32)4 – (42)0 + (52)3
= 1 × 38 – (4)0 + 56
= 38 – 1 + 56
(d) [(2)-3 ÷ (2)-8] × [(32)-2 ÷ (3)-4]
= (2)-3/(2)-8 × (3)-4/(3)-4
= (2)-3+8 × (3)-4+4
= 25 × 30
= 25 × 1
= 25
(e) (-6)2 × 3-4 × 12/9 × (32)3
= 62 × 3-4 × 6 × 2/(3)2 × (3)6
= 62+1 × 2 × 3-4/(3)2+6
= 2 × 63/38+4
= 2 × 63/312
= 2 × (3 × 2)3/312
= 24/39
(f) (34)-3 – 20 × (32)4 + (20)2
= 3-12 – 1 × (3)8 + (2)0
= 3-12 × (3)8 + 1
= 3-12+8 + 1
= 3-4 + 1
Question no – (9)
Solution :
(a) (2x2)3/(5x)-2
= (2x2)3 (5x)2
= 8x6 × 25x2
= 200x8
(b) (5y/(4x)2)3
= 53y3/(4x)6
= 125y3/4096x6
(c) (6a2b2)3 + (3a2)4
= 216a6b6 + 81a8
(d) 2a2 (a2 + 3a – a3)
= 2a4 + 6a3 – 2a5
Question no – (10)
Solution :
(a) 5-2 × 32/5-4 × 3-6
= 54 × 32 × 36/52
= 54-2 × 32+6
= 52 × 38
(b) x-2 × y-4 × z-3/xyz
= 1/x2 × y4 × z3 × xyz
= 1/x3y5z4
(c) (-3)2 × (52)-2
= (-3)2/(25)2
= 32/(25)2
(d) [(-42)3 ÷ (2)2)4] × (32)-2
= [(-4)6 ÷ (2)8] × 1/32
= 46/28 × 1/32
= (22)6/28 × 1/32
= 212/28 × 1/32
= 212-8/32
= 24/32
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