aⁿ = a × a × a × ... (n times)

Calculation rules

1. •[object Object],: aᵐ × aⁿ = aᵐ⁺ⁿ
2. •[object Object],: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
3. •[object Object],: (aᵐ)ⁿ = aᵐⁿ
4. •[object Object],: (ab)ⁿ = aⁿbⁿ
5. •[object Object],: (ab)ⁿ = aⁿ/bⁿ

Special exponents

• a⁰ = 1 (if a ≠ 0)
• •a¹ = a
• a⁻ⁿ = 1aⁿ
• a^(12) = √a
• •a^(mn) = ⁿ√(aᵐ)

√a is the positive number whose square equals a.

Properties

1. •√(a × b) = √a × √b
2. •√(ab) = √a / √b
3. •(√a)² = a
4. •√(a²) = |a|

Simplification

√48 = √(16 × 3) = 4√3

a × 10ⁿ where 1 ≤ a < 10