Year 10: Integer indices

This cheat sheet covers integer indices, a key concept in Algebra. Understanding this topic will help you with many future mathematical concepts.

What are Integer Indices?

Integer indices are a shorthand way of writing repeated multiplication. They represent a number raised to a power.

Rules of Integer Indices

• xⁿ = x * x * ... * x (n times)
• x^m * xⁿ = x^m+n (When multiplying, add the indices)
• x^m / xⁿ = x^m-n (When dividing, subtract the indices)
• (x^m)ⁿ = x^m*n (When raising to a power, multiply the indices)
• x⁰ = 1 (Any number (except 0) raised to the power of 0 is equal to 1)
• 0⁰ does not have an agreed-upon value

Examples

Example 1: 2³ = 2 * 2 * 2 = 8

Example 2: 3² * 4² = 9 * 16 = 144

Example 3: 5⁴ / 5² = 625 / 25 = 25