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

**RD Sharma Solutions for Class 9 Maths Chapter 2 – Exponents of Real Numbers** 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 x^{n} = 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

### 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(a ^{4} b^{3})^{10} x 5 (a^{2} b^{2})^{3}**

**(ii) (2x ^{-2} y^{3})^{3}**

**Solution:**

Using laws: (a^{m})^{n} = a^{mn} , a^{0} = 1, a^{-m} = 1/a and a^{m} x a^{n} = a^{m+n}]

**(i)** 3(a^{4} b^{3})^{10} x 5 (a^{2} b^{2})^{3}

On simplifying the given equation, we get;

= 3(a^{40} b^{30}) x 5 (a^{6} b^{6})

= 15 (a^{46} b^{36})

^{m})

^{n}= a

^{mn}and a

^{m}x a

^{n}= a

^{m+n}]

**(ii) **(2x ^{-2} y^{3})^{3}

On simplifying the given equation, we get;

= (2^{3} x ^{-2 × 3} y^{3×3})

= 8 x ^{-6} y^{9}

**(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;

= 3^{3 }+ (−2)^{−2}

= 3^{3} + (−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} = (5^{4})^{-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 x^{n} = 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} ÷ x^{n} = 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}

= (5^{4 })^{ 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?

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

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

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