The NCERT Solutions for Class 8 Mathematics Chapter 12, focusing on Exponents and Powers, provide invaluable assistance to students aiming for excellence in their examinations. These solutions, aligned with the CBSE curriculum, offer a comprehensive understanding of the concepts presented in the chapter.

Students can access the NCERT Solutions for Class 8 Maths Chapter 12: Exponents and Powers. Curated by experts according to the CBSE syllabus for 2023–2024, these step-by-step solutions make Maths much easier to understand and learn for the students. These solutions can be used in practice by students to attain skills in solving problems, reinforce important learning objectives, and be well-prepared for tests.

Question 1 :

**Evaluate:**

**(i) 3-2 **

**(ii) (-4)-2 **

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

Answer :

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

= 1/9

(ii) (-4)-2 = (1/-4)2

= 1/16

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

= 25

= 32

Question 2 :

**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**

Answer :

(i)(30+4– 1)×22 = (1+(1/4))×22

= ((4+1)/4 )×22

= (5/4)×22

= (5/22)×22

= 5×2(2-2)

= 5×20

= 5×1 = 5

(ii)(2-1×4-1)÷2-2

= [(1/2)×(1/4)] ÷(1/4)

= (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

= 2(-1×-2)+3(-1×-2)+4(-1×-2)

= 22+32+42

= 4+9+16

=29

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

= 1

(v) {(-2/3)-2}2 = (-2/3)-2×2

= (-2/3)-4

= (-3/2)4

= 81/16

Question 3 :

**Evaluate:**

**(i) (8-1×53)/2-4**

**(ii) (5-1×2-2)×6-1 **

Answer :

(i) (8-1×53)/2-4

=

= 2×125 = 250

(ii) (5-1×2-2)×6-1

= (1/10)×1/6

= 1/60

Question 4 :

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

Answer :

5m ÷ 5-3 = 55

5(m-(-3) ) = 55

5m+3 =55

Comparing exponents on both sides, we get

m+3 = 5

m = 5-3

m = 2

Question 5 :

**Simplify the following:**

**(i) **

**(ii) **

Answer :

(i)

=

=

(ii)

=

=

=

=

= 1×1×3125

= 3125

Question 6 :

**Simplify and express the result in power notation with a 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**

Answer :

(i)

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

= (-4)5-8

= 1/(-4)3

(ii) (1/23)2

= 12/(23)2

= 1/23×2 = 1/26

(iii) -(3)4×(5/3)4

= (-1)4×34×(54/34 )

= 3(4-4)×54

= 30×54 = 54

(iv)

= (3-7/3-10)× 3-5

= 3-7 – (-10) × 3-5

= 3(-7+10)×3-5

= 33×3-5

= 3(3+-5)

= 3-2

=1/32

(v) 2-3×(-7) – 3

= (2×-7)-3

(Because am×bm = (ab)m)

= 1/(2×-7)3

= 1/(-14)3

Question 7 :

**Evaluate:**

**(i) **

**(ii) **

Answer :

(i)

= 3-4

= -1

(ii)

=

=

=

= 512/125

Question 1 :

**Express the following numbers in standard form.**

**(i) 0.0000000000085**

**(ii) 0.00000000000942**

**(iii) 6020000000000000**

**(iv) 0.00000000837**

**(v) 31860000000**

Answer :

(i) 0.0000000000085 = 0.0000000000085×(1012/1012) = 8.5 ×10-12

(ii) 0.00000000000942 = 0.00000000000942×(1012/1012) = 9.42×10-12

(iii) 6020000000000000 = 6020000000000000×(1015/1015) = 6.02×1015

(iv) 0.00000000837 = 0.00000000837×(109/109) = 8.37×10-9

(v) 31860000000 = 31860000000×(1010/1010) = 3.186×1010

Question 2 :

**Express the following numbers in the usual form.**

**(i) 3.02×10-6**

**(ii) 4.5×104**

**(iii) 3×10-8**

**(iv) 1.0001×109**

**(v) 5.8×1012**

**(vi) 3.61492×106**

Answer :

(i) 3.02×10-6 = 3.02/106 = 0 .00000302

(ii) 4.5×104 = 4.5×10000 = 45000

(iii) 3×10-8 = 3/108 = 0.00000003

(iv) 1.0001×109 = 1000100000

(v) 5.8×1012 = 5.8×1000000000000 = 5800000000000

(vi) 3.61492×106 = 3.61492×1000000 = 3614920

Question 3 :

**Express the number appearing in the following statements in standard form.**

**(i) 1 micron is equal to 1/1000000 m.****(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb.****(iii) Size of bacteria is 0.0000005 m****(iv) Size of a plant cell is 0.00001275 m****(v) Thickness of a thick paper is 0.07 mm**

Answer :

(i) 1 micron = 1/1000000

= 1/106

= 1×10-6

(ii) Charge of an electron is 0.00000000000000000016 coulombs

= 0.00000000000000000016×1019/1019

= 1.6×10-19 coulomb

(iii) Size of bacteria = 0.0000005

= 5/10000000 = 5/107 = 5×10-7 m

(iv) Size of a plant cell is 0.00001275 m

= 0.00001275×105/105

= 1.275×10-5m

(v) Thickness of a thick paper = 0.07 mm

0.07 mm = 7/100 mm = 7/102 = 7×10-2 mm

Question 4 :

**In a stack, there are 5 books, each having a thickness of 20 mm and 5 paper sheets, each having a thickness of 0.016 mm. What is the total thickness of the stack?**

Answer :

Thickness of one book = 20 mm

Thickness of 5 books = 20×5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016×5 = 0.08 mm

Total thickness of a stack = 100+0.08 = 100.08 mm

= 100.08×102/102 mm

mm

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The NCERT solution for class 8 Chapter 12: Exponents and Powers is important as it provides a structured approach to learning, ensuring that students develop a strong understanding of foundational concepts early in their academic journey. By mastering these basics, students can build confidence and readiness for tacking more difficult concepts in their further education

Yes, the NCERT solution for class 8 Chapter 12: Exponents and Powers is quite useful for students in preparing for their exams. The solutions are simple, clear, and concise allowing students to understand them better. Exponents and Powers ally, they can solve the practice questions and exercises that allow them to get exam-ready in no time.

You can get all the NCERT solutions for class 8 Maths Chapter 12 from the official website of the Orchids International School. These solutions are tailored by subject matter experts and are very easy to understand.

Yes, students must practice all the questions provided in the NCERT solution for class 8 Maths Chapter 12 : Exponents and Powers as it will help them gain a comprehensive understanding of the concept, identify their weak areas, and strengthen their preparation.

Students can utilize the NCERT solution for class 8 Maths Chapter 12 effectively by practicing the solutions regularly. Solve the exercises and practice questions given in the solution. Also, you can make Exponents and Powers al notes and jot down the important concepts for your understanding.