What is a Math Case Study on Exponents and Powers for Class 8?

A Math Case Study on Exponents and Powers for Class 8 helps students understand laws of exponents, powers, and standard form through real-life examples and solved questions aligned with the CBSE and ICSE syllabus.

How can students prepare for Class 8 Exponents and Powers case study questions?

Students can prepare for Class 8 Exponents and Powers case study questions by practicing NCERT-based worksheets, watching video tutorials, and solving PDF examples to strengthen conceptual understanding.

What are the important laws of exponents in Class 8 mathematics?

The important laws of exponents for Class 8 include product law, quotient law, power of a power, and zero exponent law. These rules simplify mathematical calculations and appear in case study questions frequently.

Where can I download Class 8 Maths Exponents and Powers case study PDFs?

You can download Class 8 Maths Exponents and Powers case study PDFs from educational platforms offering free study materials, practice sets, and solved examples for CBSE and ICSE students.

How do video tutorials help in understanding Exponents and Powers for Class 8?

Video tutorials simplify complex topics in Exponents and Powers by providing step-by-step visual explanations. They make learning interactive and help students solve Class 8 maths case study questions easily.

Math Case Study on Exponents and Powers for Class 8

In modern communication systems, satellites play a crucial role in transmitting signals across vast distances. These satellites orbit the Earth at heights that are often expressed in scientific notation because the values involved are extremely large. For instance, a geostationary satellite orbits approximately \(3.6 \times 10^7\) meters above the Earth’s surface. Engineers also work with very small numbers such as the wavelength of the signal, which might be around \(2.5 \times 10^{-2}\) meters. While designing systems, engineers must use the laws of exponents to simplify calculations involving frequency, power, and signal strength. The use of powers of 10 helps in maintaining accuracy and ease in computation. Understanding and applying exponent rules and scientific notation ensures that data transmission remains precise and efficient in real-world applications like GPS, television broadcasting, and internet communication.

1. The height of a geostationary satellite is \(3.6 \times 10^7\) m. The wavelength of a signal is \(2.5 \times 10^{-2}\) m. What is the ratio of the height of the satellite to the wavelength of the signal?

(A) \(1.44 \times 10^{9}\)

(B) \(1.44 \times 10^{8}\)

(D) \(9.0 \times 10^{8}\)

Solution:

\[ \frac{3.6 \times 10^7}{2.5 \times 10^{-2}} = 1.44 \times 10^{(7 – (-2))} = 1.44 \times 10^{9} \]

2. The power of a signal is given by \(5 \times 10^{-3}\) W and is amplified by \(2 \times 10^{3}\) times. What is the new power of the signal?

(A) \(1.0 \times 10^{0}\) W

(B) \(1.0 \times 10^{1}\) W

(D) \(1.0 \times 10^{-1}\) W

Solution:

\[ (5 \times 10^{-3}) \times (2 \times 10^{3}) = 10 \times 10^{0} = 1.0 \times 10^{0} \text{ W} \]

3. The distance between two satellites is \(2.4 \times 10^5\) m and the average signal speed is \(3 \times 10^8\) m/s. How much time (in seconds) does the signal take to travel between them?

(A) \(8.0 \times 10^{-4}\)

(B) \(8.0 \times 10^{-4}\)

(D) \(9.0 \times 10^{-4}\)

Solution:

\[ t = \frac{\text{distance}}{\text{speed}} = \frac{2.4 \times 10^5}{3 \times 10^8} = 0.8 \times 10^{-3} = 8.0 \times 10^{-4} \text{ s} \]

4. A satellite transmits signals with a power of \(1.2 \times 10^5\) W. If the signal power decreases to \(3 \times 10^{-3}\) of its value when it reaches Earth, what is the received power?

(A) \(3.6 \times 10^{2}\) W

(B) \(3.6 \times 10^{1}\) W

(D) \(3.6 \times 10^{-1}\) W

Solution:

\[ 1.2 \times 10^5 \times 3 \times 10^{-3} = 3.6 \times 10^{2} \text{ W} \]

5. A satellite is \(3.6 \times 10^7\) m above Earth and another is \(7.2 \times 10^7\) m. Find the ratio of their altitudes in simplest form.

(A) \(1 : 2\)

(B) \(2 : 1\)

(D) \(4 : 3\)

Solution:

\[ \frac{3.6 \times 10^7}{7.2 \times 10^7} = \frac{1}{2} \Rightarrow 1 : 2 \]

Math Case Study on Exponents and Powers for Class 8

Math Case Study on Exponents and Powers for Class 8

Key Concepts of Exponents and Powers

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Case Study 5: Math Case Study on Exponents and Powers for Class 8

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