Class 8 → Mathematics → Chapter 2: Power Play (New Course)

I. Chapter Summary

This chapter introduces the concept of powers (exponents) and their role in simplifying large numbers and calculations. Students learn how to express numbers in exponential form, understand laws of exponents, and apply them in problem-solving. The chapter also explains negative exponents, powers of 10, and their applications in scientific notation. These concepts are essential for algebra, scientific calculations, and real-life applications involving very large or very small quantities.

II. Key Concepts Covered

1. Powers (Exponents)

• A power represents repeated multiplication of a number.
• Example: $2^3 = 2 \times 2 \times 2 = 8$

2. Base and Exponent

• Base: Number being multiplied
• Exponent: Number of times multiplication occurs

3. Laws of Exponents

• $a^m \times a^n = a^{m+n}$
• $a^m \div a^n = a^{m-n}$
• $(a^m)^n = a^{mn}$
• $a^0 = 1 \quad \text{(where } a \neq 0\text{)}$
• $a^{-n} = \frac{1}{a^n}$​

4. Powers of 10

• Used to express large numbers easily
• Example: $1000 = 10^3$

5. Scientific Notation

• Writing numbers in the form:
  $a \times 10^n \quad \text{where } 1 \leq a < 10$
• Example: $5000 = 5 \times 10^3$

6. Simplification Using Exponents

• Helps in solving complex expressions easily.

III. Important Questions

(A) MCQs (1 Mark)

1. $2^4 = 16$
   (a) 8 (b) 16 (c) 32 (d) 64
   Answer: (b) 16
2. $10^3 = 1000$
   (a) 100 (b) 1000 (c) 10 (d) 1
   Answer: (b) 1000
3. $a^3 \times a^2 = a^{3+2} = a^5$
   (a) $a^5$ (b) $a^6$ (c) $a^1$ (d) $a^0$
   Answer: (a) a5a^5a5
4. $5^0 = 1$
   (a) 0 (b) 1 (c) 5 (d) 10
   Answer: (b) 1

(B) Short Answer Questions (2/3 Marks)

1. Express 64 as a power of 2.
2. Simplify: $3^4 \times 3^2 = 3^{4+2} = 3^6$
3. Write 0.0005 in scientific notation.
4. Find the value of $(2^3)^2 = 2^{3 \times 2} = 2^6$

(C) Long Answer Questions (5 Marks)

1. Explain the laws of exponents with suitable examples.
2. Simplify: $(5^3 \times 5^2) \div 5^4 = 5^{3+2-4} = 5^1 = 5$
3. Express 7500000 in scientific notation and explain the steps.
4. Solve: $(2^5 \times 2^3) \div 2^4 = 2^{5+3-4} = 2^4 = 16$

(D) HOTS Questions

1. If $a^x \times a^y = a^{12}$ and $x – y = 2$, find the values of $x$ and $y$.
2. A number is written as $4^3 \times 5^3 = (4 \times 5)^3 = 20^3$. Express it as a single power.

IV. Key Formulas / Concepts

• $a^m \times a^n = a^{m+n}$
• $a^m \div a^n = a^{m-n}$
• $(a^m)^n = a^{mn}$
• $a^0 = 1$
• $a^{-n} = \frac{1}{a^n}$​

Example:

• $2^3 = 8, \quad 10^4 = 10000$

V. Deleted Portions (CBSE 2025–2026)

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026)

Note: This is an estimate. Actual marks distribution may vary.

VII. Previous Year Questions (PYQs)

1 Mark

• Evaluate $3^3$. (CBSE 2020)

2/3 Marks

• Simplify $2^5 \times 2^3 = 2^{5+3} = 2^8 = 256$. (CBSE 2019)

5 Marks

• Express numbers in scientific notation and explain the method. (CBSE 2018)

VIII. Real-World Application Examples

• Scientific Calculations: Used in astronomy for large distances.
• Computers: Binary system uses powers of 2.
• Finance: Compound interest uses exponents.
• Physics & Chemistry: Used in formulas and measurements.

IX. Student Tips & Strategies for Success

Time Management

• Practice exponent rules daily.
• Revise formulas regularly.

Exam Preparation

• Memorize laws of exponents.
• Solve previous year questions.

Stress Management

• Stay consistent with practice.
• Break complex problems into steps.

X. Career Guidance & Exploration (Class 8 Level)

• Important for careers in:
  • Engineering & Technology
  • Data Science & AI
  • Finance & Economics
• Helps build strong analytical and logical thinking skills.

XI. Important Notes

• Follow NCERT textbook examples carefully.
• Practice different types of exponent problems.
• Focus on understanding laws rather than memorizing blindly.
• Refer to official CBSE updates regularly.