Positive Indices and the Basic Rules

What is an index?

The index (or power/exponent) tells us how many times to multiply the base by itself.

Example: 5³ = 5 × 5 × 5 = 125.

Rule 1: Multiplying

a^m × aⁿ = a^m+n

Example: x² × x⁵ = x²⁺⁵ = x⁷.

Rule 2: Dividing

a^m ÷ aⁿ = a^m-n

Example: y⁷ ÷ y³ = y^7-3 = y⁴.

Rule 3: Power of a Power

(a^m)ⁿ = a^{m × n}

Example: (2³)² = 2^{3 × 2} = 2⁶ = 64.

Tip: The base must be the same before you can add or subtract the indices.

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