Frank ICSE Class 8 Solutions Chapter 2

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Frank ICSE Mathematics Class 8 Solutions Chapter 2 Exponents

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Frank ICSE Mathematics Class 8 Math Book, Chapter 2, Exponents. Here students can easily find step by step solutions of all the problems for Exponents, Exercise 2.1 and 2.2 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 2 solutions. Here in this post all the solutions are based on latest Syllabus.

Exponents Exercise 2.1 Solution :

Question no – (1)

Solution :

(a) 6-9

= 1/69

(b) 4-11

= 4-11
= 1/411

(c) (3/4)-5

= (4/3)5

(d) (-4/7)-12

= (- 4/7)-12

= (7/-4)2

(e) (9/10)-13

= (9/10)-13

= (10/9)13

Question no – (2)

Solution :

(a) 5-7

= 5-8

= 1/58

(b) (54)

= 512 ÷ 5

= 513

Question no – (3)

Solution :

= 83 is the multiplicative inverse of 8-3

Question no – (4)

Solution :

= 10100 ÷ 10 is the same as 1099

Question no – (5)

Solution :

(a) 64 in exponential form

= 26

(b) 1/243 in exponential form

= 3-5

(c) -125/8 in exponential form

= (- 5/2)3

(d) 1296 in exponential form

= 64

(e) 16/81 in exponential form

= (2/3)4

(f) 625/256 in exponential form

= (5/4)4

(g) – 81/16 in exponential form

= (- 3/2)4

(h) – 216/343 in exponential form

= (- 6/7)3

Question no – (6)

Solution :

(a) (2)-3

= 1/8

The value is 1/8

(b) (- 3)4

= 81

The value is 81

(c) (- 5)-3

= 1/-125

The value is 1/-125

(d) (1/2)5

= 1/32

The value is = 1/32

(e) (1/3)-3

= 27

The value is 27

Question no – (7)

Solution :

(a) We have 28 × 1019 and 3 × 1020

During both with 1019 we get 28 and (3 × 10) = 30

Among then 28 <3a

So, clearly, 2 × 1020 is larger than 8 × 10-13

(b) We have 2 × 10-12 and 8 × 10-13

Multiplying both with 1013, we get 2 × 10 and 8

Among them 20 > 8

So, clearly 2 × 10-12 is greater than 8 × 10-13

Question no – (8)

Solution :

(a) Given, (5)3 × (5)-8 × (5)-11

= (5)3-8-11

= (5)-15….(Simplified)

(b) Given, (-6)4 × 35 ÷ 2-4

= (- 6)4 × 35 × 24

= 39 × 28  ….(Simplified)

(c) Given, 32 × 2-3 × (1/4)-2

= 32 × 2-3 × 24

= 32 × 2

= 18 ….(Simplified)

(d) Given, (5)-4 × (4/5)-4 × 28

= (4)-4 × 28

= 2-8 × 28

= 1 ….(Simplified)

(e) Given, (-3)4 × (- 3)8

= (- 3)9 × (- 3)-4

= (-3)9-4

= (- 3)5 ….(Simplified)

Question no – (9)

Solution :

(a) Given in the question,

= {(1/3)-3 – (1/2)-3} ÷ (1/4)-3

Now,

= {(1/3)-3 – (1/2)-3} ÷ (1/4)-3

= {33 – 23} × 43

= (27 – 8) × 64

= 19 × 64

= 1216

Thus, the value is 1216.

(b) In the question

= {(1/3)-1 × (- 9)-1}-1

Now,

= {(1/3)-1 × (- 9)-1}-1

= {3 × 1/9}-1

= {1/-3}-1

= – 3

Therefore, the value is -3

(c) From the question we get,

= (52 – 32) × (2/3)2

Now,

= (52 – 32) × (2/3)2

= (25 – 9) × 4/9

= 16 × 4/9

= 64/9

Hence, the value is 64/9

(d) In the question,

= {(2/3)2}3 × (1/3)-4 × (3)-2 × (2)-1

Now,

= {(2/3)2}3 × (1/3)-4 × (3)-2 × (2)-1

= 64/729 × 81 × 1/9 × 1/2

= 32/81

Therefore, the value is 32/81

(e) (4-1 ÷ 6-1)3

= (1/4 × 6)3

= (3/2)3

= 27/8

Therefore, the value is 27/8

Question no – (10)

Solution :

(a) (2-1 + 3-1 + 4-1)0

= (1/2 + 1/3 + 1/4)0

= (13/12)0

= 1

(b) (2-1 + 3-1 + 4-1)0

= (1/2 + 1/3 + 1/4)0

= (13/12)0

= 1

(c) In the given question,

= {(2° + 3-1) × 92}

Now,

= {(20 + 3-1) × 92}

= {1/3 × 92}

= 27

(e) In the given question,

= (5/7)-6 × (49/25)-4

Now,

= (5/7)-6 × (49/25)-4

= 25/49

(f) From the question we get,

= (4/9)-3 × (2/3)10 × (8/27)-2

Now,

= (4/9)-3 × (2/3)10 × (8/27)-2

= (2/3)-6+10-6

= (2/6)-2

= 9/4

Question no – (11)

Solution :

(a) Given, 16a3b-4c3/24a-2b2c-4

= 2/3 a5b-6c-1

(b) Given, 25a-2b2c2/6a4b-4c-2

= 5/12 a-6b6c4

(c) Given, (a2n × a3n × a4n)5

= (a9n)5

= a45n

Exponents Exercise 2.2 Solution :

Question no – (1)

Solution :

(a) 2x = 1/64

or, 2x = 1/64

or, 2x = 1/26

or, 2x = 2-6

or, x = – 6

Therefore, x = -6

(b) 162x-1 = 8x+2

Now, 162x-1 = 8x+2

or, (2)8x-4 = (2)3x + 6

or, 8x – 4 = 3x + 6

or, 5x = 10

or, x = 2

Thus, x = 2

(c) 125x-1 = 25x+2

Now, 125x-1 = 25x+2

= or, (5)3x-3 = (5)2x+4

or, 3x – 3 = 2x + 4

or, 3x – 3 = 2x + 4

or, x = 7

Hence, x = 7

(d) 125x-1 = 25x+2

Now, 125x-1 = 25x+2

= or, (5)3x-3 = (5)2x+4

or, 3x – 3 = 2x + 4

or, 3x – 3 = 2x + 4

or, x = 7

Hence, x = 7

(e) 73x+1 = 1/49

Now, 73x+1 = 1/49

or, 73x+1 = 1/72

or, 73x+1 = 7-2

or, 3x + 1 = – 2

or, 3x = – 3

or, x = – 1

Therefore, x = – 1

(f) 62x-1 × 363x-2 = 216

Now, 62x-1 × 363x-2 = 216

or, (6)2x-1 × (6)6x-4 = 63

or, (6)2x-1+6x-4 = 63

or, 8x – 5 = 3

or, 8x = 8

or, x = 1

Hence, x = 1

(g) (3/4)x+2 = (27/64)4-3x

Now, (3/4)x+2 = (27/64)4-3x

= (3/4)x+2 = (3/4)12-9x

or, x + 2 = 12 – 9x

or, 10x = 10

or, x = 1

Thus, x = 1

(h) (3-x)-2 × 3x × 81 = 1/9

Now, = (3-x)-2 × 3x × 81 = 1/9

or, (3)2x × 3x × (3)4 = 1/32

or, 32x+x+4 = 3-2

or, 3x + 4 = – 2

or, 3x = 6

or, x = 2

Therefore, x = 2

(i) 71–2x × 493 × 343 = 1/7-4

or, 71-2x × (7)6 × 73 = 74

or, 71-2x+6+3 = 74

or, 1 – 2x = 4

or, 2x = 6

or, x = 3

(j) 27x+1 = 9x+1 × 81x-2

or, (3)3x+3 = (3)2x+2 × (3)4x-8

or, (3)3x+3 =(3)2x+2+4x-8

or, 3x + 3 = 6x – 6

or, 3x = 9

or, x = 3

(k) 25x+1 = 5 × (125)x-1

or, (5)2x+2 = 5 (5)3x-3

or, (5)2x+2 = (5)1+3x-3

or, 2x + 2 = 3x – 2

or, x = 4

(l) (36)x × 68 = (216)3x-2

or, (6)2x × (6)3 = (6)9x-6

or, (6)2x+8 = (6)

or, 2x + 8 = 9x – 6 or, 7x = 14

or, x = 2

(m) (125)y-4 = (25)y-2

or, (5)3y – 12 = (5)2y-4

or, 3y – 12 = 2y – 4

or, y = 8

(n) (27)7+1 = (9)y+3

or, (3)3y+3 (3)2y+6

or, 3y + 3 = 2y + 6

or, y = 3

(o) (2/5)x-2 = (25/4)3

or, (2/5)x-2 = (5/2)6

or, (2/5)x-2 = (2/5)-6

or, x – 2 = – 6

or, x = – 4

(p) (2/3)x-8 = (8/27)x

or, (3/2)x-8 = (2/3)3x

or, (3/2)x-8 = (3/2)-3x

or, x- 8 = – 3x

or, 4x = 8

or, x = 2

Question no – (2)

Solution :

(a) (2/3)-4 × (2/3)3

or, (2/3)-12 = (2/3)4m

or, 4m = – 12

or, m = – 3

(b) (2/7)-17 ÷ (2/7)8 = (2/7)2m+1

or, (2/7)-17-8 = (2/7)2m+1

or, – 25 = 2m + 1

or, 2m = – 26

or, m = – 13

(c) (3/5)-3 × (3/5)10 = (3/5)3m+1

or, (3/5)7 = (3/5)3m+1

or, 3m + 1 = 7

or, 3m = 6

or, m = 2

(d) (4/5)3m+1 × (4/5)-15 = (4/5)m

or, (4/5)3m-14 = (4/5)m

or, 3m – 14 = m

or, 2m = 14

or, m = 7

Question no – (3)

Solution :

(a) 106/57 × 25

= 56 × 26/57 × 25

= 2/5

(b) 67/25 × 36

= 27 × 37/25 ×36

= 22 × 3/1

= 12

(c) 82 × 93/65

= 26 × 36/25 × 35

= 2 × 3

= 6

Question no – (4)

Solution :

(a) [(2/3)-2]3

= (2/3)-6

= (3/2)6

= 729/64

(b) (2x– 3)4 × (x4)3

= 2x-12 × x12

= 2

(c) 22n-1 × 41-n

= 22n-1 × 22n-1+2-2n

= 21

= 2

(d) (73)4 × (7-2)5

= 712 × 7-10

= 712-10

= 72

= 49

(e) (23 × 3-2)-2

= 2-6 × 34

= 34/26

= 81/64

(f)  64n × (4)2-3n

= (4)3n × (2)2-3n

= (4)3n+2-3n

= 42

= 16

(g) (5-2)4 × (125)2

= (5)-8 × (53)2 = 5-8+6

= 5-2

= 1/25

(h) (9-5)2 ÷ 27-6

= 9-10 ÷ 3-18

= 3-20 ÷ 318

= 3-2

= 1/9

Revision Exercise Questions Solution :

Question no – (1)

Solution :

(a) (7/8)-3 × (7/8)2

To evaluate the given problem,

= (7/8)-3 × (7/8)2

= (7/8)-3+2

= 8/7

(b) [(5/4)-1 – (5/3)-1] ÷ (7/5)-2

To evaluate the given problem,

= [(5/4)-1 – (5/3)-1] ÷ (7/5)-2

= [4/5 – 3/5] ÷ (5/7)2

= [1/5] × 49/25

= 49/125

Question no – (2)

Solution :

(a) (2/3)3x+1 × (2/3)3 = (2/3)10

We need to find,

= x = ?

= (2/3)3x+1 × (2/3)3 = (2/3)10

= (2/3)3x+1 × (2/3)3 = (2/3)10

or, (2/3)3n+4 = (2/3)3

or, 3x + 4 = 3

or, 3x = -1

or, x = -1/3

(b) (25)x+2 = 5x-4 × 125x

Here we find the x

(25)x+2 = 5x-4 × 125x

or, (5)2x+4 = 5x-4 × (5)3x

or, (5)2x+4 = (5)4x-4

or, 2x + 4 = 4x – 4

or, 2x = 8

or, x = 4

Thus, here we find the x = 4

Question no – (3)

Solution :

(a) (-2/3)-3 ÷ (4/27)-2

To evaluate the given problem,

= (-2/3)-3 ÷ (4/27)-2

= (-3/2)3 ÷ (27/4)2

= – 27/8 × 16/721

= – 2/27

(b) (9/4)-2 ÷ (2/3)3 + 4 (2/7)0

Now we evaluate the given problem by

= (9/4)-2 ÷ (2/3)3 + 4 (2/7)0

= (4/9)2 × (3/2)3 + 4.1

= 16/81 × 27/8 + 4

= 2/3 + 4

= 16/3

Question no – (4)

Solution :

(a) (5)× (5)8 × (5)11

= 53+8+11

= 522

(b) (- 6)4 × 35 ÷ 24

= (6)4 × 35/24 = 34 × 24 × 35/24

= 34 × 35 = 39

(c) 32 × 2-3 × (1/4)-2

= 32 × 1/23 × (4/1)2

= 32 × 1/23 × 16

= 32 × 2

= 18

(d) (5)-4 × (4/5)-4 × 28

= 1/54 × 54/44 × 28

= 28/44

= 28/28

= 1

Question no – (5)

Solution :

723 + 724 + 725 + 726/16

Now to simplify the given problem,

= 723 + 724 + 725 + 726/16

= 723 (1 + 7 + 72 + 73)/16

= 723 (1 + 7 + 49 + 343)/16

= 723 (400)/16

= 723 × 25

Next Chapter Solution :

Updated: June 24, 2023 — 6:20 am