lightbulb Key Concepts

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1. Laws of Exponents

• aᵐ · aⁿ = aᵐ⁺ⁿ
• (aᵐ)ⁿ = aᵐⁿ
• (ab)ⁿ = aⁿbⁿ
• aᵐ / aⁿ = aᵐ⁻ⁿ
• a⁰ = 1

2. Radicals and Rational Exponents

The n-th root of a is written as ⁿ√a = a^(1/n).

• ⁿ√(ab) = ⁿ√a · ⁿ√b
• ⁿ√(a/b) = ⁿ√a / ⁿ√b
• (ⁿ√a)ᵐ = ⁿ√(aᵐ) = a^(m/n)