Indices
ICSE · Class 9 · Mathematics
Quick revision notes for Indices — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- If m is a positive integer, then a × a × a × ... (m times) = aᵐ
- In aᵐ, 'a' is called the base and 'm' is called the power, exponent, or index
- aᵐ is read as 'a raised to the power m' or 'a power m'
Laws of Indices
- First Law (Product Law): When multiplying powers with same base, add the exponents
- Second Law (Quotient Law): When dividing powers with same base, subtract the exponents
- Third Law (Power Law): When raising a power to another power, multiply the exponents
Special Types of Indices
- Zero Exponent: Any non-zero number raised to power 0 equals 1
- Negative Exponent: aⁿ = 1/a⁻ⁿ and a⁻ⁿ = 1/aⁿ
- Fractional Exponent: a¹/ⁿ = ⁿ√a and aᵐ/ⁿ = ⁿ√aᵐ
Simplification Techniques
- Express all terms with the same base when possible
- Convert radicals to exponential form for easier manipulation
- Use prime factorization to identify common bases
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