Year 10: Integer indices

This cheat-sheet covers integer indices in Year 10 Algebra.

Key Concepts

• What is an Integer Index? An integer index (also known as a power) indicates how many times a base is multiplied by itself. For example, x³ means x * x * x.
• x⁰ = 1 Any non-zero number raised to the power of 0 is equal to 1.
• x^-n = 1/xⁿ A negative integer index means taking the reciprocal of the base raised to the positive integer index.
• x^-n = 1 ÷ xⁿ For example, 2^-3 = 1 ÷ 2³ = 1 ÷ 8 = 0.125

Rules and Formulas

• (x^m)ⁿ = x^m*n Raise the entire power to another power.
• x^m * xⁿ = x^m+n Add the integer indices when multiplying terms with the same base.
• x^m / xⁿ = x^m-n Subtract the integer indices when dividing terms with the same base.

Examples

Example 1: 2⁴ * 2² = 2⁶ = 64

Example 2: 5³ / 5¹ = 5² = 25