What is an Exponents and Powers Case Study for Class 8?

An Exponents and Powers Case Study for Class 8 helps students understand the laws of exponents, powers, and standard form. It includes practical examples, solved exercises, and CBSE-based questions to strengthen conceptual understanding.

Where can I download the Exponents and Powers Case Study Class 8 PDF?

You can download the Exponents and Powers Case Study Class 8 PDF from trusted educational websites offering free CBSE resources, worksheets, and solved question sets for students.

What are the key concepts in Exponents and Powers for Class 8?

The key concepts in Exponents and Powers for Class 8 include product law, quotient law, zero exponent law, and expressing numbers in standard form. These are covered in CBSE Class 8 case study questions.

How can video tutorials help with Class 8 Exponents and Powers?

Video tutorials explain each concept of Exponents and Powers with clear examples. They help Class 8 students solve case study questions step-by-step and enhance understanding of CBSE maths topics.

Why should students solve Exponents and Powers Case Study Questions?

Solving Exponents and Powers Case Study Questions helps Class 8 students improve problem-solving skills, understand the laws of exponents, and apply mathematical reasoning to real-life problems effectively.

Exponents and Powers Case Study Class 8 PDF

In a renewable energy project, a team of students decided to analyze the efficiency of solar panels installed on their school rooftop. Each solar panel produces \(2.4 \times 10^3\) watts of power on average during peak sunlight hours. The school has installed \(4 \times 10^2\) such panels. During an energy exhibition, the students had to present the total power output in standard form and compare it with the power produced by a local wind turbine, which generates \(9.6 \times 10^5\) watts. To make accurate calculations, they also studied the effect of dust on the panels’ output, which caused a reduction factor of \(10^{-1}\) in efficiency. Using the laws of exponents, they calculated the effective power produced after the loss and presented the data in scientific notation.

1. What is the total power generated by all the panels (before efficiency loss) in standard form?

(A) \(9.6 \times 10^5\) watts

(B) \(9.6 \times 10^6\) watts

(D) \(2.4 \times 10^4\) watts

Solution:

Each panel produces \(2.4 \times 10^3\) W and there are \(4 \times 10^2\) panels. Using the law of exponents, \((2.4 \times 10^3)(4 \times 10^2) = (2.4 \times 4) \times 10^{3+2} = 9.6 \times 10^5 = 9.6 \times 10^6 \text{ W.}\)

2. If the efficiency reduces by a factor of \(10^{-1}\), what is the effective total power?

(A) \(9.6 \times 10^6\) W

(B) \(9.6 \times 10^5\) W

(D) \(9.6 \times 10^7\) W

Solution:

Effective power \(= 9.6 \times 10^6 \times 10^{-1} = 9.6 \times 10^{6-1} = 9.6 \times 10^5\) W.

3. The local wind turbine produces \(9.6 \times 10^5\) W. Compare it with the effective solar power. Which one is more powerful?

(A) Solar power is higher

(B) Both produce the same power

(D) Solar power is half of wind turbine

Solution:

Both produce \(9.6 \times 10^5\) W. Hence, they are equal.

4. If one more solar panel is added, calculate the new total power in standard form before efficiency loss.

(A) \(9.624 \times 10^6\) W

(B) \(2.4 \times 10^3\) W

(D) \(9.6 \times 10^5\) W

Solution:

New total = \(9.6 \times 10^6 + 2.4 \times 10^3 = 9.6 \times 10^6 + 0.0024 \times 10^6 = 9.6024 \times 10^6 \approx 9.624 \times 10^6\) W (approximation).

5. If each panel’s output drops to \(2.4 \times 10^2\) W on cloudy days, what is the new total power of 400 panels?

(A) \(9.6 \times 10^4\) W

(B) \(9.6 \times 10^5\) W

(D) \(8.4 \times 10^5\) W

Solution:

Total \(= 2.4 \times 10^2 \times 4 \times 10^2 = 9.6 \times 10^{2+2} = 9.6 \times 10^4\) W.

Exponents and Powers Case Study Class 8 PDF

Exponents and Powers Case Study Class 8 PDF

Key Topics Covered in the Case Study

Video Tutorials and Practice PDFs

Case Study 1: Exponents and Powers Case Study Class 8 PDF

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