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Exponents and Powers – Class 8 Extra Questions
Mathematics is a fascinating subject, dealing with various interesting numerical concepts, hypotheses, and many more. Students can emerge victorious over the vastness of the subject only through outandout practice.And that is why experienced Mathematics academicians suggest students practise solving mathematical problems regularly to gain mastery in the subject. Proper practise is the only way to get a firm grasp on the concepts and achieve excellence in Mathematics.
Quick Links
ToggleClass 8 Mathematics Chapter 12 is about Exponents and Powers. The important topics covered in this chapter are: Introduction
 Power with Negative Exponents
 Law of Exponents
 Use of Exponents to Express Small Numbers in Standard Form.
Extramarks is a reassuring website that provides trustworthy and promising NCERTrelated study materials. Our educational platform gives students the most reliable NCERT solutions, revision notes, CBSE mock tests, sample papers, CBSE past year question papers, etc., which helps students be prepared and proficient in Mathematics.
Our expert faculty members acknowledge the importance of deciphering problems to excel in Mathematics. After careful research and analysis of CBSE past year question papers and NCERT books and Exemplars, our team of experts has gathered some crucial questions in our questionbank of Important Questions Class 8 Mathematics Chapter 12. The set of important questions and solutions included in Important Questions Class 8 Mathematics Chapter 12 will help the conceptual understanding of all the topics relevant to Exponents and Power. The stepbystep solutions with required formulas provided by Extramarks for each question make it easy for students to understand the answers without much trouble.
Along with providing Important Questions Class 8 Mathematics Chapter 12, the official website of Extramarks also provides students with many other examoriented study materials. All these study materials and solutions are strictly in accordance with the latest CBSE syllabus and guidelines, making them completely trustworthy for students.
Get Access to CBSE Class 8 Maths Important Questions 202223 with ChapterWise Solutions
You can also find CBSE Class 8 Maths ChapterbyChapter Important Questions here:
CBSE Class 8 Maths Important Questions 

Sr No.  Chapters  Chapters Name 
1  Chapter 1  Rational Numbers 
2  Chapter 2  Linear Equations in One Variable 
3  Chapter 3  Understanding Quadrilaterals 
4  Chapter 4  Practical Geometry 
5  Chapter 5  Data Handling 
6  Chapter 6  Squares and Square Roots 
7  Chapter 7  Cubes and Cube Roots 
8  Chapter 8  Comparing Quantities 
9  Chapter 9  Algebraic Expressions and Identities 
10  Chapter 10  Visualising Solid Shapes 
11  Chapter 11  Mensuration 
12  Chapter 12  Exponents and Powers 
13  Chapter 13  Direct and Inverse Proportions 
14  Chapter 14  Factorisation 
15  Chapter 15  Introduction to Graphs 
16  Chapter 16  Playing with Numbers 
Important Questions Class 8 Mathematics Chapter 12 – With Solutions
Following are a few questions and their answers taken from our Important Questions Class 8 Mathematics Chapter 12. Students can get access to our question bank by registering on the official website of Extramarks.
Question 1: The human body has about 100 billion cells. This number can be written in exponential form as
 1011
 1011
 109
 109
Answer 1: Option (b) is the correct answer.
Explanation 1: 100 billion = 100,000,000,000 = 1011.
Question 2: The distance between earth and sun is 150 million kilometres which can be written in exponential form as_______________.
Answer 2: 1.5 × 108 km
Explanation 2: 1 million km = 1,000,000
Therefore, 150 million km = 150,000,000 km = 1.5 × 108 km.
Question 3: Express 27/64 and 27/64 as powers of a rational number.
Answer 3: 27 = 3 × 3 × 3 = 3³
27 = 3 × 3 × 3 = (3)³
64 = 4 × 4 × 4 = 4³
Now using the identity (a/b)m = am/bm
We get
27/64 = 3³/4³ = (3/4)³
=⟩ 27/64 = (3)³/4³ = (3/4)³
Question 4: (49 × z3) / (73 × 10 × z5) (z ≠ 0)
Answer 4: Using the identity am ÷ an = amn
(49 × z3) / (73 × 10 × z5)
= (7² × z3) / (73 × 10 × z5)
= (72+3 × z3+5) / 10
= (75 × z²) / 10
= (75z²) / 10
Question 5: Find the value of x so that
(5/3)2 × (5/3)14 = (5/3)8x
Answer 5: Using the identity am × an = am+n
We get
(5/3)2 × (5/3)14 = (5/3)8x
=⟩ (5/3)214 = (5/3)8x
Comparing the power of both sides,
=⟩ 16 = 8x
=⟩ x = 2
Question 6: Divide 293 by 10,00,000 and express the result in standard form.
Answer 6: Using the identity am = 1/am
1000000 = 106
=⟩ 293/106
= 293 × 106
= 2.93 × 106 × 10²
= 2.93 × 104
Question 7: If 53x1 ÷ 25 = 125, find the value of x.
Answer 7: 53x1 ÷ 5² = 5³
53x12 = 5³ [As am ÷ an = amn]
53x3 = 5³
Comparing the power of both sides,
3x – 3 = 3
=⟩ x – 1 = 1
=⟩ x = 2
Question 8: Simplify
(35 × 105 × 125) / (57 × 65)
Answer 8: (35 × 105 × 125) / (57 × 65)
= (35 × 105 × 5³) / (57 × (2 × 3)5)
= (35 × 25 × 55 × 5³) / (57 × 25 × 35)
[ Since, (ab)m = ambm ]
= (35 × 25 × 55+3) / (57 × 25 × 35)
= (35 × 2 5 × 52) / (57 × 25 × 35)
[Since, am × an = am+n]
35+5 × 25+5 × 52+7
= 1 × 1 × 3125
= 3125
Question 9: Express the number appearing in the following statements in standard form.
(i) Size of bacteria is 0.0000005m.
(ii) Size of a plant cell is 0.00001275m.
Answer 9: (i) Size of bacteria = 0.0000005
= 5 / 10000000
= 5 / 107
= 5 × 107 m
(ii) Size of a plant cell = 0.00001275m
= 1.275 / 100000
= 1.275 / 105
= 1.275 × 105 m
Question 10: 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?
Answer 10: If thickness of one book = 20mm
Then thickness of 5 books = 20 × 5 = 100 mm
If thickness of one paper = 0.016 mm
Then thickness of 5 papers = 0.016 × 5 = 0.08 mm
Therefore, total thickness of a stack = 100 + 0.08 = 100.08 mm
= 1.0008 × 102 mm
Question 11: Find the value of:
(i) (21 × 41) ÷ 22
(ii) (31 + 41 + 51)0
Answer 11:(i) (21 × 41) ÷ 22
= [(1/2) × (1/4)] ÷ (1/4)
Using the identity am = 1/am
= (1 2 × 1/2²) ÷ 1/4
= 1/2³ ÷ ¼
= (1/8) × 4
= 1/2
(ii) (31 + 41 + 51)0
Using the identity a0 = 1
= 1
Question 12: Sanchay put a 1cm stick of gum through a (1 × 32) machine. How long was the stick when it came out?
Answer 12: Size of the machine= 1 × 32 = 1/3² = 1/9
Length of the stick put through the machine= 1cm.
Now we can see a negative () sign in the power means that the machine is a shrinking machine.
Therefore, 1 × 1/9 = 1/9 cm.
Thus, the length when it comes out of the machine becomes 1/9cm.
Benefits of Solving Important Questions Class 8 Mathematics Chapter 12
We’ve all heard the adage, “Practice makes perfect.”This phrase should be the main motto of any student willing to ace Mathematics. Only consistent practice can help a student get a good grasp on the concepts, theorems and hypotheses and help him feel confident in the subject. By practising questions from our question bank, Important Questions Class 8 Mathematics Chapter 12 provided on our Extramarks’ website, students will feel prepared and proficient enough for their examinations.
The following are some of the benefits of answering Class 8 Mathematics Chapter 12 Important Questions:
 Important Questions Class 8 Mathematics Class 8 Chapter 12 is a compilation of some specially chosen questions by our expert Mathematics faculty members. Our experts have prepared this question bank after analysing the CBSE past year question papers and examining several CBSE textbooks.
 All the Chapter 12 Class 8 Mathematics Important Questions have been solved with proper explanations and supported with the required formulas for the students to have an overall clarification of the concepts.
 Each question and answer in Mathematics Class 8 Chapter 12 is significant because it adheres to the most recent CBSE syllabus and CBSE guidelines, allowing students to rely on the solutions.
Besides providing Important Questions Class 8 Mathematics Chapter 12, our Extramarks’ website also provides students with the following:
 NCERT books
 CBSE revision notes
 CBSE sample papers
 Important formulas
 CBSE extra questions.
Q.1 Express 3 x 10^{7} in usual form.
Marks:1
Ans
$\begin{array}{l}3\text{\xc2}\xc3\u2014{\text{\xc210}}^{\text{7}}\text{\xc2=\xc23\xc2}\xc3\u2014\text{\xc2}\frac{1}{{10}^{7}}\text{\xc2=\xc2}\frac{3}{10000000}{\text{}}^{}\end{array}$ $\begin{array}{l}{\text{Since,\xc2 a}}^{\xe2\u201c\mathrm{m}}\text{=}\frac{1}{{\mathrm{a}}^{\mathrm{m}}}\\ \\ =\text{\xc20.0000003}\end{array}$
Q.2
$\text{Simplify}{\left(\frac{\text{2}}{\text{3}}\right)}^{\text{?7}}\text{\xd7}{\left(\frac{\text{3}}{\text{2}}\right)}^{\text{?5}}$Marks:3
Ans
$\begin{array}{l}{\left(\frac{2}{3}\right)}^{\u20197}\u2014{\left(\frac{3}{2}\right)}^{5}=\frac{{2}^{7}}{{3}^{7}}\u2014\frac{{3}^{5}}{{2}^{5}}\mathrm{Since}{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)}^{\mathrm{m}}=\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{b}}^{\mathrm{m}}}\text{}={2}^{\xe27+5}\u2014{3}^{5+7\mathrm{Since}\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}\mathrm{n}}}\end{array}$
Q.3 Find x such that (2)^{x+1} × (2)^{5} = (2)^{7}.
Marks:2
Ans
(2)^{x + 1 + 5} = (2)^{7} â‡’ (2)^{x + 6} = (2)^{7}
On both the sides powers have the same base different from 1 and 1, their exponents must be equal.
âˆ´ x + 6 = 7
â x = 7 â6 = 1
Q.4 What is the standard form of 0.000561?
${\text{a5.61 \xd7 10}}^{?5}$ ${\text{b5.61 \xd7 10}}^{?4}$ ${\text{c5.61 \xd7 10}}^{4}$ ${\text{d5.61 \xd7 10}}^{5}$Marks:1
Ans [ 2050625 ]
Q.5
$\text{If}{\left(\frac{\mathrm{x}}{\mathrm{y}}\right)}^{\mathrm{a}?1}={\left(\frac{\mathrm{y}}{\mathrm{x}}\right)}^{\mathrm{a}?3},\text{whatisthevalueofa}?$a1
b2
c3
d4
Marks:1
Ans [ 2050842 ]
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CBSE Class 8 Maths Important Questions
FAQs (Frequently Asked Questions)
1. How many questions are there in Important Questions Class 8 Chapter 12, and what are the topics covered?
Our experienced mathematics academicians have very carefully picked some essential questions for our question bank Important Question Class 8 Chapter 12. There are many questions varying from very shorttype to very longtype. These questions will help students understand the types and levels of questions they need to practise to be well prepared for their examinations.
The topics that have been covered in Important Questions Class 8 Mathematics Chapter 12 are:
 Introduction
 Power with Negative Exponents
 Law of Exponents
 Use of Exponents to Express Small Numbers in Standard Forms.
2. What is the blueprint of the Mathematics Class 8 question paper?
Following is the blueprint of the Mathematics Class 8 question paper:
 There are at least ten very shortanswertype questions at the beginning of the question paper. These ten questions carry one mark each. Hence, the total weightage of this section is 10 marks.
 Next in the question paper are the shortanswertype questions which are at least six in number. These shorttype questions carry two marks each. Hence, the total weightage of this section is 12 marks.
 Next on the question paper are the shortanswertype2 questions, which are six in number. These questions carry three marks each. Hence, the total weightage of this section is 18 marks.
 The final section consists of six longanswer questions.These questions carry five marks eachHence, the total weightage of this section is 30 marks.
Therefore there will be 28 questions in the question paper with a total of 70 marks.