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RD Sharma Solutions for Class 9 Maths Chapter 2 Exponents of Real Numbers
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RD Sharma Solutions for Class 9 Maths Chapter 2 Exponents of Real Numbers

Chapter 2 of RD Sharma’s Class 9 Maths deals with the concept of exponents of real numbers. Exponents, also known as powers, are used to express numbers in a more convenient form. This chapter covers various properties and rules of exponents, which help simplify mathematical expressions and calculations. In this chapter, we will learn about exponents with real numbers, laws of exponents, and how to apply these laws to solve problems effectively.

RD Sharma Solutions for Class 9 Maths Chapter 2 Exponents of Real Numbers

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 9 Chapter 2 Exponents of Real Numbers PDF.

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RD Sharma Solutions for Class 9 Maths Chapter 2: Exponents of Real Numbers (Exercise-Wise)

RD Sharma Solutions for Class 9 Maths Exercise 2.1

Q1. Simplify: (x³)²
A1. Using the law of exponents (a^m)^n = a^{m \times n}, we get: 
(x³)² = x⁶
 
Q2. Simplify: \frac{a^5}{a^2}
A2. Using the law \frac{a^m}{a^n} = a^{m-n}, we get: 
\frac{a^5}{a^2} = a^{5-2} = a³
 
Q3. Simplify: (3a²)³
A3. Using the law (ab)^m = a^m b^m, we get: 
(3a²)³ = 3³ × (a²)³ = 27a⁶

 

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RD Sharma Solutions for Class 9 Maths Exercise 2.2

Q1. Simplify: (x^4) \times (x^5)
A1. Using the law of exponents a^m \times a^n = a^{m+n}, we get: 
(x⁴) × (x⁵) = x⁹
 
Q2. Simplify: \frac{b^7}{b^3} \times b^4
A2. First, simplify the first part using the division law \frac{b^m}{b^n} = b^{m-n}: 
\frac{b^7}{b^3} = b^{7-3} = b⁴ 
Now multiply it by b^4: 
b⁴ × b⁴ = b⁸
 
Q3. Simplify: (2x²y³)²
A3. Using the law (ab)^m = a^m b^m, we get: 
(2x²y³)² = 2² × (x²)² × (y³)² = 4x⁴y⁶

 

RD Sharma Solutions for Class 9 Maths Exercise 2.3

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Q1. Simplify: (5x²y³)⁴
A1. Using the law (ab)^m = a^m b^m, we get: 
(5x²y³)⁴ = 5⁴ × (x²)⁴ × (y³)⁴ = 625x⁸y¹²
 
Q2. Simplify: \frac{m^6}{m^3}
A2. Using the law \frac{a^m}{a^n} = a^{m-n}, we get: 
\frac{m^6}{m^3} = m^{6-3} = m³
 
Q3. Simplify: (a⁻³ × b⁴)²
A3. Using the law (ab)^m = a^m b^m, we get: 
(a⁻³ × b⁴)² = a⁻⁶ × b⁸

 

RD Sharma Solutions for Class 9 Maths Exercise 2.4

Q1. Simplify: (2x⁻³)²
A1. Using the law (a^m)^n = a^{m \times n}, we get: 
(2x⁻³)² = 2² × (x⁻³)² = 4x⁻⁶
 
Q2. Simplify: \frac{x^{-2}}{x^{-4}}
A2. Using the law \frac{a^m}{a^n} = a^{m-n}, we get: 
\frac{x^{-2}}{x^{-4}} = x^{-2-(-4)} = x²
 
Q3. Simplify: (a⁻³ × b⁴)²
A3. Using the law (ab)^m = a^m b^m, we get: 
(a⁻³ × b⁴)² = a⁻⁶ × b⁸

 

RD Sharma Solutions for Class 9 Maths Exercise 2.5

Q1. Simplify: \frac{a^3}{a^{-2}}
A1. Using the law \frac{a^m}{a^n} = a^{m-n}, we get: 
\frac{a^3}{a^{-2}} = a^{3-(-2)} = a⁵
 
Q2. Simplify: (x⁻¹)³
A2. Using the law (a^m)^n = a^{m \times n}, we get: 
(x⁻¹)³ = x⁻³
 
Q3. Simplify: (3x⁻²y⁵)⁻¹
A3. Using the law (a^m)^{-1} = a^{-m}, we get: 
(3x⁻²y⁵)⁻¹ = 3⁻¹x²y⁻⁵ = 1/3 x² y⁻⁵
 

Why RD Sharma Class 9 Chapter 2 Maths is Important

Chapter 2 of Class 9 Maths in RD Sharma, Exponents of Real Numbers, is important for several reasons:

  1. Foundation for Advanced Concepts: Exponents are the building blocks for many advanced topics in algebra, including quadratic equations, polynomials, and logarithms. A strong understanding of exponents in Class 9 will make it easier to grasp these more complex topics in higher classes.
  2. Application in Real Life: Exponents are used in various real-life applications, such as compound interest calculations, scientific notation, and population growth models. Learning how to work with exponents helps students understand and solve real-world problems.
  3. Helps in Competitive Exams: Many competitive exams, including JEE and NEET, include questions on exponents. A thorough understanding of the topic can boost a student’s ability to tackle these exams effectively.
  4. Simplifies Complex Problems: Exponents simplify large calculations by turning repeated multiplication into simpler expressions. This helps save time and reduces errors when solving math problems.
  5. Strengthens Mathematical Thinking: Mastering the laws and properties of exponents helps students develop strong logical and problem-solving skills, which are essential for success in mathematics and other subjects.
  6. Improves Calculation Speed: Understanding the laws of exponents, like the product rule, quotient rule, and power rule, enables students to solve problems quickly and efficiently, which is essential for exams and assignments.

In summary, RD Sharma's Chapter 2 on Exponents of Real Numbers is crucial for building a solid mathematical foundation, preparing for future topics, and excelling in exams.

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RD Sharma Solutions for Class 9 Maths Chapter 2: Exponents of Real Numbers

In Chapter 2 of the Class 9 RD Sharma Solutions, students will learn key concepts about Exponents of Real Numbers, including:

  • Introduction to Exponents of Real Numbers
  • Integral Exponents of Real Numbers
  • Laws of Integral Exponents
  • Rational Exponents of Real Numbers
  • nth Root of a Positive Real Number
  • Laws of Rational Exponents

For a detailed explanation of these concepts from the RD Sharma textbook, visit BYJU’S website. We also offer CBSE sample papers, previous year question papers, and CBSE notes to help you prepare and score well in your upcoming board exams.

Conclusion

Exponents are an essential part of mathematics, and understanding how to work with them is crucial for solving algebraic and other mathematical problems. RD Sharma’s solutions for Class 9 Chapter 2 provide a clear and detailed explanation of the rules and laws of exponents. By practicing the examples in the book, students can master these concepts and perform well in exams.

To sum up, remember these key points:

  • Exponents make repeated multiplication easier to handle.

  • Always apply the correct exponent rule.

  • Negative exponents and zero exponents have special meanings.

  • Fractional exponents represent roots.

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    FAQs on RD Sharma Solutions for Class 9 Maths Chapter 2

    Why should we download RD Sharma Solutions for Class 9 Maths Chapter 2?

    Downloading RD Sharma Solutions for Chapter 2 helps students get access to detailed step-by-step solutions for all the problems in the chapter. It simplifies learning and helps in understanding difficult concepts in Maths.

    Does the IL website provide answers to RD Sharma Solutions for Class 9 Maths Chapter 2 in a detailed way?

    Yes, the IL website provides detailed and easy-to-understand answers for RD Sharma Solutions Chapter 2, making it easier for students to grasp the concepts and solve problems effectively.

    Give an overview of concepts present in RD Sharma Solutions for Class 9 Maths Chapter 2.

    Chapter 2 of Class 9 RD Sharma covers the topic of Exponents of Real Numbers. The concepts include understanding the laws of exponents, how to simplify expressions with exponents, and working with both positive and negative powers.

    What topics are covered in RD Sharma Class 9 Maths Chapter 2 on Exponents of Real Numbers?

    The chapter covers:

    • The definition and meaning of exponents

    • Laws of exponents (product, division, and power laws)

    • Negative exponents and zero exponents

    • Simplification of expressions using exponent rules

    • Solving problems involving exponents of real numbers

    How can RD Sharma Class 9 Solutions for Maths Chapter 2 help students?

    The solutions provide clear and detailed explanations of each topic, helping students understand and solve problems more easily. It also boosts confidence in handling complex questions by breaking them down into simple steps.

    Can RD Sharma Class 9 Solutions for Maths Chapter 2 be used for exam preparation?

    Yes, RD Sharma Solutions Chapter 2 is a great resource for exam preparation. It covers all the important concepts and problems that are likely to appear in exams, making revision easier and more effective.

    Can RD Sharma Class 9 Solutions for Maths Chapter 2 be used for self-study?

    Absolutely! The solutions are ideal for self-study as they explain concepts clearly and guide you through solving the problems step by step, making it easier to learn independently.

    When to use Chapter 2 Class 9 RD Sharma Solutions?

    You can use RD Sharma Solutions when you’re studying the chapter on Exponents of Real Numbers, practicing problems, or revising for exams. It helps in gaining clarity on concepts and improving problem-solving skills.

    Is it good to use the RD Sharma Class 9 Solutions Chapter 2?

    Yes, it’s highly recommended to use RD Sharma Class 9 Solutions Chapter 2 for comprehensive learning. It’s a trusted resource for understanding the fundamentals of exponents and applying them correctly in problems.

    Where to download Chapter 2 Class 9 RD Sharma Solutions?

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    Is RD Sharma Class 9 Solutions Chapter 2 free to download?

    Yes, RD Sharma Solutions for Class 9 Chapter 2 are available for free download on various educational platforms.

    Can I use Class 9 RD Sharma Chapter 2 Solutions for exam preparation?

    Yes, RD Sharma Chapter 2 Solutions are a great tool for exam preparation. They cover all the essential topics and help you practice problems effectively to improve your understanding and performance in exams.