NCERT Solutions For Class 7 Maths Chapter 11 Exponents And Powers Exercise 11.3 - 2025-26
FAQs on NCERT Solutions For Class 7 Maths Chapter 11 Exponents And Powers Exercise 11.3 - 2025-26
1. What is the correct step-by-step method to solve problems using the law of exponents for multiplying powers with the same base (aᵐ × aⁿ) in Chapter 11?
The NCERT Solutions for Class 7 Maths Chapter 11 explain this method as follows:
First, identify the terms with the same base.
Keep the base the same and add the exponents (m + n).
Write the result as a single power. For example, to solve 3² × 3⁴, you keep the base as 3 and add the exponents 2 and 4 to get 3⁶.
This method simplifies calculations and is fundamental for solving complex expressions.
2. How do the NCERT Solutions for Class 7 Maths Chapter 11 guide students to express large numbers in standard form?
The NCERT solutions provide a clear procedure for expressing numbers in standard form (k × 10ⁿ), where 1 ≤ k < 10. The steps are:
Move the decimal point to the left until there is only one non-zero digit before it. This gives you the value of 'k'.
Count the number of places the decimal point was moved. This count becomes the exponent 'n' for the power of 10.
For example, the number 5,98,00,000 is written as 5.98 × 10⁷, because the decimal was moved 7 places to the left.
3. According to the NCERT Solutions, what is a common mistake when simplifying expressions like (5²)³ versus 5² × 5³?
A common mistake is confusing the rules for 'power of a power' and 'multiplying powers'. The NCERT solutions clarify this distinction:
For (5²)³, you must apply the rule (aᵐ)ⁿ = aᵐⁿ. Here, you multiply the exponents: 5²ˣ³ = 5⁶.
For 5² × 5³, you must apply the rule aᵐ × aⁿ = aᵐ⁺ⁿ. Here, you add the exponents: 5²⁺³ = 5⁵.
The solutions emphasize that understanding this difference is key to correctly simplifying exponential expressions.
4. Why is it important to follow the step-by-step methods in the NCERT Solutions for Exponents and Powers?
Following the step-by-step methods is crucial because it ensures accuracy and builds a strong conceptual foundation. The laws of exponents are not just shortcuts; they represent logical mathematical principles. By applying these steps consistently, you:
Avoid common calculation errors, especially with large numbers.
Learn the correct methodology prescribed by the CBSE 2025-26 curriculum for scoring full marks.
Develop the logical reasoning needed for more advanced topics in algebra in higher classes.
5. How does the concept of a zero exponent (a⁰ = 1) work, and why is this rule essential for solving problems in Chapter 11?
The rule a⁰ = 1 can be understood using the division law of exponents. For any non-zero number 'a', if you divide a power by itself, like aᵐ ÷ aᵐ, the result is 1. Using the law of exponents, this is aᵐ⁻ᵐ = a⁰. Therefore, a⁰ = 1. This rule is essential in simplifying complex expressions where terms might cancel each other out, ensuring that expressions like (3⁵ ÷ 3⁵) correctly simplify to 3⁰, which is 1.
6. Can the laws of exponents be applied if the bases are different but the exponents are the same? How do NCERT Solutions address this?
Yes, there is a specific law for this scenario. The NCERT solutions demonstrate the rule aᵐ × bᵐ = (ab)ᵐ. This means if two different bases are raised to the same exponent and are being multiplied, you can multiply the bases first and then apply the exponent to the product. For instance, 2³ × 4³ is solved by first multiplying the bases (2 × 4 = 8) and then applying the exponent, resulting in 8³. This method is a key problem-solving technique in the chapter exercises.
7. Beyond exams, what is the real-world importance of expressing numbers in standard form, as explained in Chapter 11?
Expressing numbers in standard form is not just an academic exercise; it has immense practical value, especially in science and engineering. This method is used to write and compare very large or very small quantities easily. For example:
Astronomers use it to denote the distance between planets (e.g., the distance from Earth to the Sun is approx. 1.496 × 10⁸ km).
Biologists use it to express the size of microscopic cells or viruses.
This makes numbers more manageable, reduces the chance of errors in calculation, and simplifies the comparison of values at a massive scale.
