Year 8: Simplification of algebraic expressions involving integer indices

This cheat-sheet helps you simplify algebraic expressions that use integer indices (powers).

Key Concepts

• What is an Index? The number written as a superscript (^) next to a base. For example, x² means x multiplied by itself (x × x).
• Rules for Simplification:
• xⁿ × x^m = x^n+m (When multiplying with the same base, add the indices.)
• x^m / xⁿ = x^m-n (When dividing with the same base, subtract the indices.)
• x⁰ = 1 (Any number to the power of 0 equals 1.)
• x^-n = 1 / xⁿ (A negative index means the reciprocal of the expression raised to the positive index.)

Examples

Example 1:x² × x³ = x⁵

Example 2:x⁴ / x² = x²

Example 3:x^-2 = 1 / x²

Important Notes

Remember to always simplify expressions from the top down. Pay close attention to adding and subtracting indices.