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

Class 9: Maths Chapter 2 solutions. Complete Class 9 Maths Chapter 2 Notes.

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

RD Sharma 9th Maths Chapter 2, Class 9 Maths Chapter 2 solutions

Exercise 2.1

Question 1: Simplify the following

(i) 3(a⁴ b³)¹⁰ x 5 (a² b²)³

(ii) (2x ^-2 y³)³

Solution:

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

(ii) (2x ^-2 y³)³

On simplifying the given equation, we get;

= (2³ x ^{-2 × 3} y^3×3)

= 8 x ^-6 y⁹

(iii)

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

(i) a^a+ b^b

(ii) a^b + b^a

(iii) (a+b)^ab

Solution:

(i) a^a+ b^b

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

= 3³ + (−2)⁻²

= 3³ + (−1/2)²

= 27 + 1/4

= 109/4

(ii) a^b + b^a

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

Solution:

(i) L.H.S. =

= R.H.S.

(ii) We have to prove here;

L.H.S. =

=R.H.S.

(iii) L.H.S. =

Question 4: Prove that

Solution:

(i) L.H.S

= R.H.S.

(ii) L.H.S

= R.H.S.

Question 5: Prove that

Solution:

(i) L.H.S.

= R.H.S.

(ii)

L.H.S.

= R.H.S.

Question 6: If abc = 1, show that

Solution:

Exercise 2.2

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

Solution:

Question 2: Simplify

Solution:

Question 3: Prove that

Solution:

(i) L.H.S.

=R.H.S.

Question 4.

Show that:

Solution:

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: x^m x xⁿ = x^{m +n}

Question 3: State the quotient law of exponents.

Solution:

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

Mathematically: x^m ÷ xⁿ = x^{m – n}

Question 4: State the power law of exponents.

Solution:

Power law of exponents :

(x^m)ⁿ = x^{m x n} = x^mn

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

Solution:

Question 6: Write the value of {5(8^1/3 + 27^1/3 ) ³}^1/4 .

Solution:

{5(8^1/3 + 27^1/3 ) ³}^1/4

= {5(2^3×1/3 + 3^3×1/3 ) ³}^1/4

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

= (5⁴ ) ^1/4

= 5

RD Sharma Solutions for Class 9 Maths Chapter 2: Download PDF

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

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

Chapterwise RD Sharma Solutions for Class 9 Maths :

• Chapter 1–Number System
• Chapter 2–Exponents of Real Numbers
• Chapter 3–Rationalisation
• Chapter 4–Algebraic Identities
• Chapter 5–Factorization of Algebraic Expressions
• Chapter 6–Factorization Of Polynomials
• Chapter 7–Introduction to Euclid’s Geometry
• Chapter 8–Lines and Angles
• Chapter 9–Triangle and its Angles
• Chapter 10–Congruent Triangles
• Chapter 11–Coordinate Geometry
• Chapter 12–Heron’s Formula
• Chapter 13–Linear Equations in Two Variables
• Chapter 14–Quadrilaterals
• Chapter 15–Area of Parallelograms and Triangles
• Chapter 16–Circles
• Chapter 17–Construction
• Chapter 18–Surface Area and Volume of Cuboid and Cube
• Chapter 19–Surface Area and Volume of A Right Circular Cylinder
• Chapter 20–Surface Area and Volume of A Right Circular Cone
• Chapter 21–Surface Area And Volume Of Sphere
• Chapter 22–Tabular Representation of Statistical Data
• Chapter 23–Graphical Representation of Statistical Data
• Chapter 24–Measure of Central Tendency
• Chapter 25–Probability

About RD Sharma

RD Sharma isn't the kind of author you'd bump into at lit fests. But his bestselling books have helped many CBSE students lose their dread of maths. Sunday Times profiles the tutor turned internet star
He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like 'series solution of linear differential equations'. Meet Dr Ravi Dutt Sharma — mathematics teacher and author of 25 reference books — whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it's only recently that a spoof video turned the tutor into a YouTube star.

R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. "I like to spend all my time thinking and writing about maths problems. I find it relaxing," he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government's Guru Nanak Dev Institute of Technology.

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