Mathematics · Class 7
Exponents and Powers
Laws of exponents with integral powers and scientific notation.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Exponents show repeated multiplication. Learn laws of exponents with integers, standard form for very large and small numbers — used in science notation.
Laws of Exponents
Product
aᵐ × aⁿ = aᵐ⁺ⁿ
Quotient
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power of power
(aᵐ)ⁿ = aᵐⁿ
Zero exponent
a⁰ = 1 (a ≠ 0)
Negative Exponents
- a⁻ⁿ = 1/aⁿ
- Express very small numbers with negative powers of 10
Standard Form
Write as k × 10ⁿ where 1 ≤ k < 10. Earth's mass ~ 5.97 × 10²⁴ kg uses standard form.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Simplify
Simplify 2³ × 2⁵.
- 1Same base: add exponents
- 22³⁺⁵ = 2⁸
Answer
2⁸ = 256
Example 2: Standard Form
Write 3,40,00,000 in standard form.
- 13.4 × 10⁷
Answer
3.4 × 10⁷
Key Points to Remember
- ✓ Base same for combining exponents
- ✓ Negative exponent means reciprocal
- ✓ Standard form for astronomy and microbiology
Exam Tips
- • Write base explicitly when ambiguous
- • Count decimal shifts for powers of 10
Practice MCQs — Exponents and Powers
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
10⁵ ÷ 10² equals: