Rules of Integers and Exponents

Integers and exponents are important concepts in mathematics that are used to perform various mathematical operations. Understanding the rules of integers and exponents is crucial for solving mathematical problems effectively. Here are some key rules and properties related to integers and exponents:

Rules of Integers:
1. Addition of Integers:
- When adding two positive integers, the sum will be positive.
- When adding two negative integers, the sum will be negative.
- When adding a positive integer and a negative integer, subtract their absolute values and keep the sign of the larger integer.

2. Subtraction of Integers:
- Subtracting a positive integer from another positive integer will result in a positive difference.
- Subtracting a negative integer from another negative integer will result in a positive difference.
- Subtracting a negative integer from a positive integer is the same as adding their absolute values and keeping the sign of the larger integer.

3. Multiplication of Integers:
- The product of two positive integers is positive.
- The product of two negative integers is positive.
- The product of a positive and a negative integer is negative.

4. Division of Integers:
- Dividing a positive integer by a positive integer results in a positive quotient.
- Dividing a negative integer by a negative integer results in a positive quotient.
- Dividing a positive integer by a negative integer or vice versa results in a negative quotient.

Rules of Exponents:
1. Product Rule:
- To multiply two exponents with the same base, add their exponents.
- For example, a^m * a^n = a^(m+n).

2. Quotient Rule:
- To divide two exponents with the same base, subtract their exponents.
- For example, a^m / a^n = a^(m-n).

3. Power Rule:
- To raise an exponent to another exponent, multiply their exponents.
- For example, (a^m)^n = a^(m*n).

4. Zero Rule:
- Any number (except zero) raised to the power of zero is equal to 1.
- For example, a^0 = 1, where a ≠ 0.

5. Negative Exponent Rule:
- A negative exponent indicates the reciprocal of the base raised to the positive exponent.
- For example, a^(-n) = 1 / a^n.

RD Sharma Solutions for Class 7 Mathematics:
RD Sharma solutions for Class 7 Mathematics are comprehensive study materials that provide step-by-step explanations and solutions for the textbook questions. These solutions are designed to help students understand the concepts and solve problems effectively. Some key features of RD Sharma solutions for Class 7 Mathematics are:

- Detailed explanations: The solutions provide detailed explanations for each question, making it easier for students to grasp the concepts.

- Practice questions: The solutions include additional practice questions to reinforce the understanding of the topics.

- Clear and concise: The solutions are written in a clear and concise manner, making them easy to understand and follow.

- Chapter-wise organization: The solutions are organized chapter-wise, allowing students to focus on specific topics and track their progress.

- Step-by-step approach: The solutions follow a step-by-step approach, guiding students through the problem-solving process.

- Visual aids: