RD Sharma Class 9 Solutions Chapter 2 - Exponents of Real Numbers Exercise 2.1

All the numbers that are found in the real world are real numbers. Numbers are everywhere around us. For example, natural numbers are used for counting purposes, rational numbers are used for denoting fractions, irrational numbers are used for finding the square root of a number and integers are used for measuring temperature etc. All these different types of numbers collectively make real numbers. In this chapter, we will learn all about real numbers and their exponents. Real numbers can be defined as numbers that consist of both rational as well as irrational numbers. In simple words, real numbers include positive and negative integers along with irrational numbers. Any number that we can think of, except the complex numbers, is a real number. The set of real numbers is generally denoted by R.

Now, a question arises, which numbers are not real numbers? The answer to this question is - ‘numbers that are neither rational nor irrational are non-real numbers’  for example - √-1, 2 + 3i, and -i. These numbers include the set of complex numbers which is denoted by C.

Laws of Exponents

Exponents can also be defined as Powers or Indices. In simple words, the exponent of a number tells how many times we have to multiply the number by itself. It is very important to understand how the laws of exponents work. These laws are given below.

1. Product Law

According to the product law of exponents if we are multiplying two numbers that are having the same base then we can add the exponents.

                                                       a^m × aⁿ = a ^m+n     

where a, m and n are natural numbers. One thing that we should keep in mind is that the base should be the same. 

2. Quotient Law

According to the quotient law of exponents, if we divide two numbers with the same base then their exponents are subtracted. To divide two exponents that have the same base value, subtract the power in the denominator from the power in the numerator. For example, 

                                         a^m aⁿ = an ^m−n

where a, m and n all are natural numbers and the base should be the same in both the quantities.

3. Power Law

According to the power law of exponents if a number raises power to a power, then the exponents are multiplied.

                     (a^m)ⁿ = a^m×n

In the above-given example, there is one base ‘a’ and two exponents m and n.  

RD Sharma Solutions for Class 9 Maths Chapter 2 – Exponents of Real Numbers helps the students in understanding concepts like integral exponents of a real number, laws of exponents and rational powers easily and effectively. RD Sharma promotes easy learning for the students thus helping students understand the concepts of exponents of Real Numbers. The book provides in-depth solutions for Class 9 Maths Chapter 2 and helps in improving method based learning in the mind of the student from an early age. The students who want to score more marks in the examination are suggested to go through the book to solve their doubts

RD Sharma Solutions Class 9 Maths Chapter 2 provides a clear and concise explanation of each concept in a simple and easy to understand language. These solutions have been generally designed keeping in mind the student’s grasping skills to solve the CBSC Class 9 Maths problems with ease.