# NCERT Solutions For Class 8 Maths Chapter 12 Exponents and Powers

## Class 8 Maths Chapter 12 Exponents and Powers

NCERT Solutions For Class 8 Maths Chapter 12 Exponents And Powers, (Maths) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions withinside the very last asked from those.

Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions.  To assist students, solve all of the questions and maintain their studies without a doubt, we have provided step by step NCERT Solutions for the students for all classes.  These answers will similarly help students in scoring better marks with the assist of properly illustrated Solutions as a way to similarly assist the students and answering the questions right.

## Exercise 12.1

Page No: 197

1. Evaluate:

(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5

Solution:

(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

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

(i) (-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)

= (-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

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

= ((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

4. Evaluate

(i) (8-1×53)/2-4

(ii) (5-1×2-2)×6-1

Solution:

(i) (8-1×53)/2-4

= 2×125 = 250

(ii) (5-1×2-2)×6-1

= (1/10)×1/6

= 1/60

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

Solution:

5m ÷ 5-3 = 55

5(m-(-3) ) = 55

5m+3 =55

Comparing exponents both sides, we get

m+3 = 5

m = 5-3

m = 2

6. Evaluate

(i)

(ii)

Solution:

(i)

= 3-4

= -1

(ii)

=  512/125

7. Simplify.

(i)

(ii)

Solution:

(i)

=

=

(ii)

= 1×1×3125

= 3125

## Exercise 12.2

Page No: 200

1. Express the following numbers in standard form.

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

Solution:

(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

2.Express the following numbers in 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

Solution:

(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) 3.61492×10= 3.61492×1000000 = 3614920

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

Solution :

(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

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

Solution:

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

Benefits of NCERT Solutions for Class 8

NCERT Solutions for Class 8 contains extremely important points, and for each chapter, each concept has been simplified to make it easier to remember and increase your chances of achieving excellent exam results. Exam Preparation References Here are some tips on how these Solutions can help you prepare for the exam.

1. This helps students solve many of the problems in each chapter and encourages them to make their concepts more meaningful.
2. NCERT Solutions for Class 8 encourage you to update your knowledge and refine your concepts so that you can get good results in the exam.
3. These NCERT Solutions For Class 8 are the best exam materials, allowing you to learn more about your week and your strengths. To get good results in the exam, it is important to overcome your weaknesses.
4. Most of the questions in the exam are formulated in a similar way to NCERT textbooks. Therefore, students should review the Solutions in each chapter in order to better understand the topic.
5. It is free of cost.

Tips & Strategies for Class 8 Exam Preparation

1. Plan your course and syllabus and make time for revision
2. Please refer to the NCERT Solutions available on the cbsestudyguru website to clarify your concepts every time you prepare for the exam.
3. Use the cbsestudyguru learning app to start learning to successfully pass the exam. Provide complete teaching materials, including resolved and unresolved tasks.
4. It is important to clear all your doubts before the exam with your teachers or Alex (an Al study Bot).
5. When you read or study a chapter, write down algorithm formulas, theorems, etc., and review them quickly before the exam.
6. Practice an ample number of question papers to make your concepts stronger.
7. Take rest and a proper meal.  Don’t stress too much.

Why opt for cbsestudyguru NCERT Solutions for Class 8 ?

• cbsestudyguru provide NCERT Solutions for all subjects at your fingertips.
• These Solutions are designed by subject matter experts and provide Solutions to every NCERT textbook questions.
• cbsestudyguru especially focuses on making learning interactive, effective and for all classes.
• We provide free NCERT Solutions for class 8 and all other classes.