NCERT Solutions for class 8 Maths Chapter 12 Exponents and Powers Exercise 12.1

The NCERT solutions is aimed at mastering the concepts and acquiring comprehensive knowledge about the various types of questions asked in CBSE Class 8 Mathematics. Students can access a set of questions and answers for all the NCERT textbook exercise 12.1, prepared by BYJU’S subject experts here. Download NCERT Solutions for Maths Chapter 12 and start practising to score well.

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Access Other Exercise Solutions of Class 8 Maths Chapter 12 Exponents and Powers

Exercise 12.2 Solutions: 4 Questions (Short answers)

Access Answers to NCERT Class 8 Maths Chapter 12 Exponents and Powers Exercise 12.1 Page number 197

1. Evaluate:

(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5  

Solution:

(i) 3-2 = (1/3)2

Ncert solution class 8 chapter 12-1

= 1/9

(ii) (-4)-2 = (1/-4)2

Ncert solution class 8 chapter 12-2

= 1/16

(iii) (1/2)-5 = (2/1)5

Ncert solution class 8 chapter 12-3

= 25

= 32

2.  Simplify and express the result in power notation with positive exponent:

(i) (-4)4 ÷(-4)8   

(ii) (1/23)2  

(iii) -(3)4×(5/3)4 

(iv) (3-7÷3-10)×3-5  

(v) 2-3×(-7)-3

Solution:

(i)
Ncert solution class 8 chapter 12-4

= (-4)5/(-4)8

Ncert solution class 8 chapter 12-5

= (-4)5-8

= 1/(-4)3

(ii) (1/23)2  

= 12/(23)2

Ncert solution class 8 chapter 12-6

= 1/23×2 = 1/26

Ncert solution class 8 chapter 12-7

 

(iii) -(3)4×(5/3)4 

Ncert solution class 8 chapter 12-8
Ncert solution class 8 chapter 12-9

= (-1)4×34×(54/34 )

Ncert solution class 8 chapter 12-10

= 3(4-4)×54

Ncert solution class 8 chapter 12-11

= 30×54 = 54

Ncert solution class 8 chapter 12-12

(iv) Ncert solution class 8 chapter 12-13

=   (3-7/3-10)× 3-5

= 3-7 – (-10) × 3-5

Ncert solution class 8 chapter 12-14

= 3(-7+10)×3-5

= 33×3-5

= 3(3+-5)

Ncert solution class 8 chapter 12-15

= 3-2

=1/32

Ncert solution class 8 chapter 12-16

(v) 2-3×(-7) – 3

= (2×-7)-3

(Because am×bm = (ab)m)

= 1/(2×-7)3

Ncert solution class 8 chapter 12-17

= 1/(-14)3

3. Find the value of :

(i) (30+4-1)×22

(ii) (2-1×4-1)÷2 – 2

(iii) (1/2)-2+(1/3)-2+(1/4)-2

(iv) (3-1+4-1+5-1)0

(v) {(-2/3)-2}2

Solution:

(i)(30+4– 1)×22 = (1+(1/4))×22

Ncert solution class 8 chapter 12-18

= ((4+1)/4 )×22

= (5/4)×22

= (5/22)×22

= 5×2(2-2)

Ncert solution class 8 chapter 12-19

= 5×20

= 5×1 = 5

Ncert solution class 8 chapter 12-20

(ii)(2-1×4-1)÷2-2

= [(1/2)×(1/4)] ÷(1/4)

Ncert solution class 8 chapter 12-21

= (1/2×1/22 )÷ 1/4

= 1/23÷1/4

= (1/8)×(4)

= 1/2

(iii) (1/2)-2+(1/3)-2+(1/4)-2

= (2-1)-2+(3-1)-2+(4-1)-2

Ncert solution class 8 chapter 12-22

= 2(-1×-2)+3(-1×-2)+4(-1×-2)

Ncert solution class 8 chapter 12-23

= 22+32+42

= 4+9+16

=29

(iv) (3-1+4-1+5-1)0

= 1

Ncert solution class 8 chapter 12-24

(v) {(-2/3)-2}2 = (-2/3)-2×2

Ncert solution class 8 chapter 12-25

= (-2/3)-4

= (-3/2)4

Ncert solution class 8 chapter 12-26

= 81/16

4. Evaluate

(i) (8-1×53)/2-4

(ii) (5-1×2-2)×6-1 

 

Solution:

(i) (8-1×53)/2-4

Ncert solution class 8 chapter 12-27
Ncert solution class 8 chapter 12-28

=
Ncert solution class 8 chapter 12-29
Ncert solution class 8 chapter 12-30

= 2×125 = 250

(ii) (5-1×2-2)×6-1 

Ncert solution class 8 chapter 12-31
Ncert solution class 8 chapter 12-32

= (1/10)×1/6

= 1/60

5. Find the value of m for which 5m ÷ 5-3 = 55

Solution:

5m ÷ 5-3 = 55

5(m-(-3) ) = 55

Ncert solution class 8 chapter 12-33

5m+3 =55

Comparing exponents both sides, we get

m+3 = 5

m = 5-3

m = 2

6. Evaluate

(i) 

Ncert solution class 8 chapter 12-34

(ii) 

Ncert solution class 8 chapter 12-35

Solution:

(i)

Ncert solution class 8 chapter 12-36
Ncert solution class 8 chapter 12-37

= 3-4

= -1

(ii)

Ncert solution class 8 chapter 12-38
Ncert solution class 8 chapter 12-39

=
Ncert solution class 8 chapter 12-40
Ncert solution class 8 chapter 12-41

=
Ncert solution class 8 chapter 12-42

Ncert solution class 8 chapter 12-43 =
Ncert solution class 8 chapter 12-44
Ncert solution class 8 chapter 12-45

=  512/125

7. Simplify.

(i)     

Ncert solution class 8 chapter 12-46

(ii) 

Ncert solution class 8 chapter 12-47

Solution 7:

(i)

Ncert solution class 8 chapter 12-48

Ncert solution class 8 chapter 12-49

Ncert solution class 8 chapter 12-50

Ncert solution class 8 chapter 12-51

=
Ncert solution class 8 chapter 12-52 =
Ncert solution class 8 chapter 12-53

(ii)

Ncert solution class 8 chapter 12-54

Ncert solution class 8 chapter 12-55

Ncert solution class 8 chapter 12-56

Ncert solution class 8 chapter 12-57

=
Ncert solution class 8 chapter 12-58

Ncert solution class 8 chapter 12-59

=
Ncert solution class 8 chapter 12-60
Ncert solution class 8 chapter 12-61

=
Ncert solution class 8 chapter 12-62 =
Ncert solution class 8 chapter 12-63

= 1×1×3125
Ncert solution class 8 chapter 12-64

= 3125

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