✕✕ Exponents and Scientific Notation

Laws of Exponents

• Product: aᵐ × aⁿ = aᵐ⁺ⁿ
• Quotient: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
• Power of power: (aᵐ)ⁿ = aᵐⁿ
• Zero exponent: a⁰ = 1 (for a ≠ 0)
• Negative exponent: a⁻ⁿ = 1/aⁿ

Scientific Notation

Write very large or very small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. Example: 6.022 × 10²³ (Avogadro's number). Move the decimal point to get a between 1 and 10; count the moves as the exponent.

Multiplying in Scientific Notation

(3 × 10⁴) × (2 × 10³) = (3 × 2) × 10⁴⁺³ = 6 × 10⁷. Multiply coefficients; add exponents. Adjust if the coefficient is ≥ 10.