Year 9: Integer indices

This cheat-sheet covers integer indices. Indices represent how many times a number (the base) is multiplied by itself.

Key Concepts

• Positive Integer Index: xⁿ means x multiplied by itself n times (e.g., 2³ = 2 * 2 * 2 = 8).
• Negative Integer Index: x^-n is the reciprocal of xⁿ. (e.g., 2^-2 = 1 / 2² = 1 / 4 = 0.25).
• Zero Index: x⁰ = 1 (for any non-zero number x).

Rules

• x^m * xⁿ = x^m+n (Indices with the same base add)
• x^m / xⁿ = x^m-n (Indices with the same base subtract)
• (x^m)ⁿ = x^m*n (Indices multiply)
• x⁰ = 1

Examples

Example 1: Simplify 3² * 3⁴ = 3⁶ = 729

Example 2: Simplify x⁵ / x² = x³

Example 3: Calculate (a²)³ = a⁶

Remember: Always simplify before calculating!