Year 9: Integer indices

This cheat sheet covers integer indices - powers with negative and fractional exponents.

Key Concepts

• Integer Index: A number raised to a power, like xⁿ.
• Positive Integer Exponent: xⁿ = x * x * ... * x (n times)
• Negative Integer Exponent: x^-n = 1 / xⁿ (Inverse of xⁿ)
• Fractional Index: x^1/n = ⁿ√x (nth root of x)

Rules

• x^m * xⁿ = x^m+n (Multiplying with the same base)
• x^m / xⁿ = x^m-n (Dividing with the same base)
• (x^m)ⁿ = x^m*n (Raising a power to another power)
• (x^m * yⁿ)^m = x^m*n * y^m*n (Order of operations - BIDMAS/BODMAS)

Examples

Example 1: 2^-3 = 1 / 2³ = 1 / 8

Example 2: 3² = 3 * 3 = 9

Example 3: 4^1/2 = ²√4 = 2

Remember to simplify your answers as much as possible!