Power Play – Class 8 Mathematics notes, important questions and MCQs

Chapter overview

Exponents are a short way to write repeated multiplication. Laws of exponents and standard form make very large and very small numbers easy to handle.

Laws of exponents

• aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ.
• (ab)ⁿ = aⁿbⁿ; a⁰ = 1 (a ≠ 0); a⁻ⁿ = 1/aⁿ.
• Doubling grows fast: 2¹⁰ = 1024.

Standard form

• Write a number as k × 10ⁿ with 1 ≤ k < 10.
• Large: 3,80,000 = 3.8 × 10⁵. Small: 0.00045 = 4.5 × 10⁻⁴.
• Speed of light ≈ 3 × 10⁸ m/s.

Key terms

Base

the number being multiplied repeatedly

Exponent

how many times the base is multiplied

Standard form

k × 10ⁿ with 1 ≤ k < 10

Formulas

• aᵐ × aⁿ = aᵐ⁺ⁿ
• a⁻ⁿ = 1/aⁿ

Important questions with answers

Quick revision

• Any non-zero number to the power 0 is 1.
• 2¹⁰ ≈ one thousand.
• Standard form needs 1 ≤ k < 10.

Exam tips

• Negative exponent does not make the number negative — it makes a reciprocal.
• Count decimal moves to find the power of 10.

Practice MCQs

1. 2⁵ equals

   1. 10
   2. 25
   3. 32
   4. 64
   Show answer

   Answer: (c) 32. 2 × 2 × 2 × 2 × 2.

2. 7⁰ equals

   1. 0
   2. 1
   3. 7
   4. 70
   Show answer

   Answer: (b) 1. Any non-zero number to power 0 is 1.

3. (3²)³ equals

   1. 3⁵
   2. 3⁶
   3. 3⁹
   4. 3³
   Show answer

   Answer: (b) 3⁶. Multiply powers: 3⁶.

4. 2⁻³ equals

   1. −8
   2. 1/8
   3. −6
   4. 8
   Show answer

   Answer: (b) 1/8. 1/2³.

5. (2³)² equals

   1. 2⁵
   2. 2⁶
   3. 2⁹
   4. 4⁵
   Show answer

   Answer: (b) 2⁶. Multiply powers.

6. 0.000072 in standard form is

   1. 7.2 × 10⁻⁴
   2. 72 × 10⁻⁶
   3. 7.2 × 10⁻⁵
   4. 0.72 × 10⁻⁴
   Show answer

   Answer: (c) 7.2 × 10⁻⁵. Move the decimal 5 places.

7. (2³ × 2⁵) ÷ 2⁴ equals

   1. 2⁴
   2. 2²
   3. 2¹²
   4. 2⁶
   Show answer

   Answer: (a) 2⁴. 2⁸ ÷ 2⁴ = 2⁴.

8. 0.000 000 45 in standard form is

   1. 45 × 10⁻⁸
   2. 4.5 × 10⁻⁸
   3. 4.5 × 10⁻⁷
   4. 4.5 × 10⁷
   Show answer

   Answer: (c) 4.5 × 10⁻⁷. Move decimal 7 places.