# Concise Mathematics Class 9 ICSE Solutions for Chapter 8 - Indices

## ICSE Class 9 Mathematics Chapter 8 Selina Concise Solutions - Free PDF Download

Concise Selina Solutions Class 9 Chapter 8 is feasible for students as it helps them to score maximum marks in the examinations. The solution includes a stepwise detailed explanation of all the problems asked in the Concise Selina Solutions Class 9 Chapter 8- Indices.

These solutions are prepared by the subject experts of Vedantu, detailing the comprehensive method of solving problems. Students will be easily able to clear their doubts by understanding the concept used to solve the solutions.

Chapter 8 "Indices" includes questions on simplifying the powers and exponents of numbers and algebraic expressions. The solutions can be used by students to clear their doubts or the quick overview of revision during the process of self-study. Selina Solutions are created to help students with their exam preparation and enhance their confidence in solving difficult problems. These Selina Solutions are prepared as per the latest ICSE syllabus thus, ensuring the high possibility of scoring excellent marks in the examination.

### Concise Selina Solutions Class 9 Chapter 8 - Downloads PDF

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### What is Index?

The index in Maths Class 9 is defined as the power or the exponents raised to some number or variable. For example, 5 is the index of 2. Indices are the plural form of an index. In algebra, we usually come across exponents and variables. The constant is a value that can never be changed whereas the value assigned to some variables can be changed. In algebra, the term indices deal with the numbers. Let us learn indices and the law of indices in detail.

### Index Definition

A number or variable may include an index. The index of a variable or constant is defined as a value that is raised to the value of a variable. It represents the number of times a given number is multiplied by itself.

It is the simplest method of recording large numbers and calculations. The index states that a particular number (or variable) is to be multiplied by itself, which implies the number of times equivalent to the index raised to the base of a number.

### Law of Indices

The law of Indices is used to exhibit the numbers that have been multiplied by themselves. They can also be used to denote roots, such as the square roots and some fractions. The law of indices enables expressions including powers to be exploited more effectively than writing them comprehensively.

### Law 1: Product Law

To multiply two variables with a similar base, we need to sum up their powers and raise them to that base.

xp * xq = xp+q

Example

72 * 73 = 7 2+3 = 75

### Law 2: Quotient Law

To divide two variables with a similar base, we need to subtract the power of their denominator form the power of numerator and raise it to that base

xp / xq = xp-q

Example : x7 / x4 = x7-4 = x3

### Law 3: Power Law

When a variable with one index is further raised with another different index, then both the indices are multiplied together and raised to the power of the same base.

(xp)q = xpq

Example : (x3)4 = x12

Law 4: An index given in the form of the fraction can be represented in the radical form.

xm/n = \[\sqrt[m]{x^{n}}\] , where x is not equal to 0

Example

71/2 = \[\sqrt{7}\]

### Law 5

If a constant or variable has an index ‘0’, the result will be equal to 1, regardless of the value of the base.

X0 = 1

Example

50 = 1

### Law 6

When two variables with similar indices but with different bases are multiplied together, we need to multiply its base and raise the same index to the variable that is multiplied.

xp yq= (xy)p

Example

32.52 = (3 * 5)2 = 152

### Law 7

When two variables with similar indices but with different bases are divided together, we need to divide its base and raise the same index to the variable that is divided.

xn/m = \[\sqrt[m]{a^{n}}\]

Example

32 / 52 = (3 / 5)2

### Law 8

If the index is given in a negative value, then it can be represented as the reciprocal of the positive values raised to some variable.

x-p = 1/xp

Example: 7-1 = 1/7

### Vedantu Concise Selina Solutions Class 9 Chapter 8 Benefits

Considering the student’s understanding, the questions are divided into different levels such as easier, complex and intermediate.

The practised hand on experience of the questions given in the exercise will help a student to develop a deeper understanding of the concepts.

The questions are designed by the subject experts of Vedantu.

The questions are presented in an interesting manner so that students develop an interest in solving questions.

The questions given in the exercise provide the means of revision and preparation during exams

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