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

RD Sharma Solutions Class 9 Maths Chapter 2 – Free PDF Download

RD Sharma Solutions Class 9 Chapter 2 helps students to understand concepts like integral exponents of a real number, laws of exponents and rational powers. To facilitate easy learning and help students understand the concepts of exponents of Real Numbers, free RD Sharma solutions are provided here which can be further downloaded in the form of a PDF. Practice questions related to exponents by solving the RD Sharma Solutions for Class 9 Maths Chapter 2. To download PDF file of this material click on the below link.

BYJU’S RD Sharma Solutions Class 9 Solutions for Maths has been designed to help the students solve the CBSE Class 9 Maths problems with ease. If a is a positive real number and n is a positive integer, then the principal nth root of a is the unique positive real number x such that xn = a. The principal nth root of a is denoted by a(1/n).

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

RD Sharma Solution class 9 Maths Chapter 2 Exponents of Real Numbers 01
RD Sharma Solution class 9 Maths Chapter 2 Exponents of Real Numbers 02
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Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 2 Exponents of Real Numbers

Exercise 2.1

Question 1: Simplify the following

(i) 3(a4 b3)10 x 5 (a2 b2)3

(ii) (2x -2 y3)3

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1 Question 1

Solution:

Using laws: (am)n = amn , a0 = 1, a-m = 1/a and am x an = am+n]

(i) 3(a4 b3)10 x 5 (a2 b2)3

On simplifying the given equation, we get;

= 3(a40 b30) x 5 (a6 b6)

= 15 (a46 b36)

[using laws: (am)n = amn and am x an = am+n]

(ii) (2x -2 y3)3

On simplifying the given equation, we get;

= (23 x -2 × 3 y3×3)

= 8 x -6 y9

(iii)

RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1 Question 1 solution
RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1 Question 1 solution

Question 2: If a = 3 and b =-2, find the values of:

(i) aa+ bb

(ii) ab + ba

(iii) (a+b)ab

Solution:

(i) aa+ bb

Now putting the values of ‘a’ and ‘b’, we get;

= 33 + (−2)−2

= 33 + (−1/2)2

= 27 + 1/4

= 109/4

(ii) ab + ba

Now putting the values of ‘a’ and ‘b’, we get;

= 3−2 + (−2)3

= (1/3)2 + (−2)3

= 1/9 – 8

= −71/9

(iii) (a+b)ab

Now putting the values of ‘a’ and ‘b’, we get;

= (3 + (−2))3(−2)

= (3–2))−6

= 1−6

= 1

Question 3: Prove that

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 3

Solution:

(i) L.H.S. =

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 3 solution

= R.H.S.

(ii) We have to prove here;

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 3 solution

L.H.S. =

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 3 solution

=R.H.S.

(iii) L.H.S. =

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 3 solution

Question 4: Prove that

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 4

Solution:

(i) L.H.S

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 4 solution

= R.H.S.

(ii) L.H.S

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 4 solution

= R.H.S.

Question 5: Prove that

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 5

Solution:

(i) L.H.S.

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 5 solution

= R.H.S.

(ii)

L.H.S.

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 5 solution

= R.H.S.

Question 6: If abc = 1, show that

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 6

Solution:

RD Sharma Class 9 Chapter 2 Maths Ex 2.1 Question 6 solution

Exercise 2.2

Question 1: Assuming that x, y, z are positive real numbers, simplify each of the following:

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Solution:

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Question 2: Simplify

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Solution:

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Question 3: Prove that

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Solution:

(i) L.H.S.

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

=R.H.S.

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Question 4.

Show that:

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Solution:

RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers
RD Sharma Solutions Chapter 2 Exercise 2.2 Exponents of Real Numbers

Exercise-VSAQs

Question 1: Write (625)–1/4 in decimal form.

Solution:

(625)–1/4 = (54)-1/4 = 5-1 = 1/5 = 0.2

Question 2: State the product law of exponents:

Solution:

To multiply two parts having same base, add the exponents.

Mathematically: xm x xn = xm +n

Question 3: State the quotient law of exponents.

Solution:

To divide two exponents with the same base, subtract the powers.

Mathematically: xm ÷ xn = xm – n

Question 4: State the power law of exponents.

Solution:

Power law of exponents :

(xm)n = xm x n = xmn

Question 5: For any positive real number x, find the value of

RD Sharma Solutions for Class 9 Maths Chapter 2

Solution:

RD Sharma Solutions for Class 9 Maths Chapter 2

Question 6: Write the value of {5(81/3 + 271/3 ) 3}1/4 .

Solution:

{5(81/3 + 271/3 ) 3}1/4

= {5(23×1/3 + 33×1/3 ) 3}1/4

= { 5(2 + 3)^3}1/4

= (54 ) 1/4

= 5

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

In the 2nd chapter of Class 9 RD Sharma Solutions students will study important concepts on Exponents of Real Numbers as listed below:

  • Exponents of Real Numbers Introduction
  • Integral exponents of a Real Number
  • Laws of Integral Exponents
  • Rational Exponents of Real Number
  • nth root of a positive Real Number
  • Laws of rational exponents

To know more these concepts present in RD Sharma textbook visit BYJU’S website. We also provide CBSE sample papers, previous year question papers and CBSE notes. This will help you in scoring well in your upcoming boards.

Frequently Asked Questions on RD Sharma Solutions for Class 9 Maths Chapter 2

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

The presentation of each solution in the Chapter 2 of RD Sharma Solutions for Class 9 Maths is described in a unique way by the BYJU’S experts in Maths. The solutions are explained in understandable language which improves grasping abilities among students. To score good marks, practising RD Sharma Solutions for Class 9 Maths can help to a great extent. This chapter can be used as a model of reference by the students to improve their conceptual knowledge and understand the different ways used to solve the problems.

Is BYJU’S website providing answers to RD Sharma Solutions for Class 9 Maths Chapter 2 in a detailed way?

Yes, BYJU’S website provides answers to RD Sharma Solutions for Class 9 Maths Chapter 2 in step by step manner. This allows the students to learn all the concepts in detail and also they can clear their doubts as well. Regular practising makes them score high in Maths board exams.

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

RD Sharma Solutions for Class 9 Maths Chapter 2 has 2 exercises. The concepts of this chapter are listed below.
1. Exponents of Real Numbers Introduction
2. Integral exponents of a Real Number
3. Laws of Integral Exponents
4. Rational Exponents of Real Number
5. nth root of a positive Real Number
6. Laws of rational exponents

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