Table of Contents
In Class 8, students dive into the fascinating world of exponents and powers. This topic is essential for understanding how to express large numbers in a simpler way and perform calculations more efficiently. The laws of exponents are fundamental rules that help us manipulate expressions involving powers. In this section, we will explore the laws of exponents for Class 8, including various examples to clarify these concepts.
Students will learn about the laws of exponents with examples for Class 8, which will make it easier to grasp how to apply these rules in different mathematical situations. The laws of exponents Class 8 NCERT and CBSE syllabus for Class 8 provide a structured approach to mastering these concepts. Additionally, we will look at laws of exponents Class 8 questions that challenge students to apply what they’ve learned. For those seeking extra help, the NCERT Solutions for Class 8 Maths are a valuable resource to reinforce understanding and practice.
By the end of this chapter, students will be well-equipped to handle problems involving exponents and powers, laying a strong foundation for future math studies.
Class 8 Maths Chapter 12 Exponents and Powers PDF
In Class 8 Maths Chapter 12, we explore Exponents and Powers, which are essential concepts in mathematics. This chapter introduces the laws of exponents for class 8, helping students understand how to simplify expressions involving powers. The laws of exponents and powers class 8 provide rules that make calculations easier.
Students can find helpful resources like the Class 8 Maths Chapter 12 Exponents and Powers PDF and NCERT Solutions for Class 8 Maths to enhance their learning. Following the CBSE syllabus for class 8, this chapter lays a strong foundation for future mathematical studies.
NCERT Class 8 Maths Chapter 12 Exponents and Powers Questions with Answers
Ques: What is the value of 23?
Ans: The value of 23 is 8.
Explanation: 23 means multiplying 2 by itself three times: 2 × 2 × 2 = 8.
Ques: Simplify 52 × 53.
Ans: 52 × 53 = 52+3 = 55.
Explanation: When multiplying powers with the same base, add the exponents.
Ques: What is the value of (32)2?
Ans: (32)2 = 32 × 2 = 34 = 81.
Explanation: When raising a power to another power, multiply the exponents.
Ques: What is 10-3 as a fraction?
Ans: 10-3 = 1/103 = 1/1000.
Explanation: A negative exponent indicates the reciprocal of the base raised to the positive exponent.
Ques: Express 0.0001 in exponential form.
Ans: 0.0001 = 10-4.
Explanation: 0.0001 can be written as 10-4 since it is equal to 1/10000.
Ques: Simplify (2/3)-2.
Ans: (2/3)-2 = (3/2)2 = 9/4.
Explanation: A negative exponent flips the fraction and then raises it to the positive exponent.
Ques: What is the value of 4-2?
Ans: 4-2 = 1/42 = 1/16.
Explanation: A negative exponent indicates the reciprocal of the base raised to the positive exponent.
Ques: If x2 = 49, what is the value of x?
Ans: x = ±7.
Explanation: Taking the square root of both sides, x = ±7 because both 72 and (-7)2 equal 49.
Ques: What is the value of 20?
Ans: 20 = 1.
Explanation: Any number raised to the power of 0 is 1.
Ques: Simplify (23) × (2-5).
Ans: (23) × (2-5) = 23 + (-5) = 2-2 = 1/4.
Explanation: Add the exponents when multiplying powers with the same base, then simplify.
Ques: Write 81/3 in its simplest form.
Ans: 81/3 = 2.
Explanation: The cube root of 8 is 2.
Ques: Simplify (am) × (an).
Ans: (am) × (an) = am+n.
Explanation: When multiplying powers with the same base, add the exponents.
Ques: What is the value of 3-2?
Ans: 3-2 = 1/32 = 1/9.
Explanation: A negative exponent means taking the reciprocal of the base raised to the positive exponent.
Ques: Express 0.01 in exponential form.
Ans: 0.01 = 10-2.
Explanation: 0.01 is equivalent to 1/100, which is 10-2.
Ques: What is the value of (24) ÷ (22)?
Ans: (24) ÷ (22) = 24-2 = 22 = 4.
Explanation: Subtract the exponents when dividing powers with the same base.
Ques: What is the value of 53?
Ans: 53 = 125.
Explanation: 53 means 5 × 5 × 5 = 125.
Ques: Simplify (32 × 23).
Ans: 32 × 23 = 9 × 8 = 72.
Explanation: First, calculate each power separately, then multiply the results.
Ques: Simplify (a3)2 ÷ a4.
Ans: (a3)2 ÷ a4 = a6 ÷ a4 = a6-4 = a2.
Explanation: Multiply the exponents in the numerator, then subtract the exponent in the denominator.
Ques: What is the value of (5/2)0?
Ans: (5/2)0 = 1.
Explanation: Any number or fraction raised to the power of 0 is 1.
Ques: Simplify (25) ÷ (23).
Ans: (25) ÷ (23) = 25-3 = 22 = 4.
Explanation: Subtract the exponents when dividing powers with the same base.
Class 8 HOTS Course
The Class 8 HOTS Course enhances critical thinking and problem-solving skills through engaging activities and advanced learning techniques, ensuring academic excellence.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers
These NCERT Solutions provide students better understanding of the topics and able to score good marks in the exams. This learning material is specially created by subject matter experts with accordance to the latest CBSE syllabus given by the board. In this chapter, students will learn about how to write large numbers with ease using exponents and powers, express numbers in standard form, dealing with negative exponents, various laws of exponents and many more.
NCERT Solutions For Class 8 Maths Chapter 12 Exercises
Get detailed solution for all the questions listed under below exercises:
- 7 Questions (Short answers)
- 4 Questions (Short answers)
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers
NCERT Solutions of this chapter, Exponents and Powers tell us about the law of exponents, powers and their applications.
The main topics included are:
| Exercise | Topic |
| 12.1 | Introduction |
| 12.2 | Powers with Negative Exponents |
| 12.3 | Laws of Exponents |
| 12.4 | Use of Exponents to Express Small Numbers in Standard Form |
Key Features of NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers
- Easy and simple language used.
- NCERT Solutions will help in boosting the confidence level among students.
- Subject experts have consolidated all exercises questions at one place which could feature in your exam.
- All solutions are structured in an easy and logical language for quick revisions.
- NCERT Solutions are helpful for preparation of competitive exams.
Class 8 Maths Chapter 12 Exponents and Powers FAQs
Does these NCERT Solutions help you to clear board exams?
NCERT Solutions of this chapter designed answers with detailed descriptions according to the term limit specified by our experts. Practising these questions can help you to fetch good marks in board exams. So yes they are very helpful for board exams.
How NCERT Solutions of this chapter helps in learning exponents and powers?
NCERT Solutions of this chapter are designed by our subject matter experts in an interactive manner help the students to understand the concepts with ease. Students must go for the PDF of solutions as a major study material which helps to improve the problem solving skill.
How many questions are present in NCERT Solutions of this chapter?
This chapter contains 2 exercises. In that first one it include 7 questions and the last or second exercise contains 4 questions. So it contains total of 11 short answer questions that are present in this chapter.
