# RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions

In the RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions, students will get information about- Rational Exponents of Real Number, the nth root of a positive real number, Rational Powers, Laws of rational exponents in detail. For practice, students can prefer the following RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions PDF, prepared by our best faculties with easy and detailed solutions.

In this Exercise 2.2 of class 9 Maths, we are providing the tricks, tips, easy formulas to solve the questions speedily. The topics are all about the square roots, cube roots, and the law to rational exponents.

Learn about RD Sharma Class 9 Chapter 2 (Exponents of Real Numbers)

## Download RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions PDF

Solutions for Class 9 Maths Chapter 2 Exponents of Real Numbers Exercise 2.2

## Important Definitions RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions

As we told above, we are providing a brief on the topics. Find the complete details in the below points with examples.

1. Rational Exponents
2. The nth root of a positive real number
3. Laws of rational exponents

### Rational Exponents

Rational Exponents are also known as “Radicals.” This includes-

• Whole Number Exponent
• Fractional Exponent

#### Whole Number Exponent

The exponent of a number states how many times to apply for the number in a multiplication.

For Example-

1. 7² = 7 × 7 = 49
2. 4³ = 4 × 4 × 4 = 64

#### Fractional Exponent

As we know, the square of power doubles the exponent. But, the fractional exponent works conversely. The square of power becomes half the exponent.

For Example-

The square root of p¹ is equal to p½. In other words, p¹= √p

Similarly, the cube of power is the exponent multiplied by 3. In fractional exponent, the cube of power is the exponent divided by 3.

For Example-

The cube root of

### The nth root of a positive real number

The “nth Root” applied ‘n’ times in a multiplication provides the original value in which the 2nd root is the square root and the 3rd root is the cube root.

The root can be 2nd, 4th, 8th, 66th, 545th, etc., But, if we want to talk generally instead of saying like 2nd, 4th, etc. we say ‘nth’.

The symbol of ‘nth root’ is “n√” it is the radical symbol with a small ‘n’ with nth root.

For Example-

### Laws of Rational Exponents

Know the Laws of Rational Exponents in the below points with formulas and examples.

#### Multiplying of Powers with the Same Base

If the bases are the same, we need to add the exponents.

#### Dividing Powers with the Same Base

If the bases are the same, we need to subtract the exponent.

#### Negative Exponents

We need to change the negative exponent into a positive exponent first by making the numerator as the denominator and vice-versa.

#### Power with Exponent Zero

If the power of the exponent is zero, then the result will get ‘one’, whatever the base is.

Go through the below table to know more about the Law of Rational Exponent-