Mathematics July 22, 2026 · 10 min read

Exponents: The Language of Repeated Multiplication

Master exponents with rules, properties, and worked examples. Handle positive, negative, zero, and fractional exponents.

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Exponentiation is the mathematical operation of raising a base to a power. The notation a^b means "multiply a by itself b times." Exponents are fundamental to algebra, science, and computer science.

Key Rules

  • Product rule: a^m × a^n = a^(m+n)
  • Quotient rule: a^m ÷ a^n = a^(m-n)
  • Power rule: (a^m)^n = a^(mn)
  • Zero exponent: a^0 = 1
  • Negative exponent: a^(-n) = 1/a^n
  • Fractional exponent: a^(1/n) = ⁿ√a

Worked Examples

  1. 2^4 = 16
  2. 2^(-3) = 1/8 = 0.125
  3. 8^(2/3) = (∛8)² = 4
  4. 5^0 = 1