# Joy of Mathematics Class 8 Solutions Chapter 3

## 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 × 3

(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)or (-3)2

= – 8 or -27

(-2)> (- 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. 2× 31 × 52

= 1 ∴ 3 × 25

= 75 ≠ R.H.S. = 303 (False)

(e) L.H.S. 3= 9

R.H.S. 4= 64

L.H.S. ≠ R.H.S. (False)

(f) L.H.S. 83 × 53

= 512 × 125

= 674000

R.H.S. (10)= 10 × 10 × 10

∴ L.H.S. ≠ R.H.S. (False)

(g) L.H.S. a0 + b0 /a× b0

= 1 + 1/1 × 1

= 2/1 = R.H.S (True)

(h) L.H.S. 5 × 5= 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

Previous Chapter Solution :

Updated: May 29, 2023 — 3:15 pm