Exponent Calculator - Calculate Powers & Exponential Functions

An exponent (also called a power or index) represents repeated multiplication. In the expression aⁿ, 'a' is the base and 'n' is the exponent, meaning 'a' is multiplied by itself 'n' times.

Key Exponent Rules

• Product Rule: a^m × aⁿ = a^m+n
• Quotient Rule: a^m ÷ aⁿ = a^m-n
• Power Rule: (a^m)ⁿ = a^m×n
• Zero Exponent: a⁰ = 1 (where a ≠ 0)
• Negative Exponent: a^-n = 1 / aⁿ
• Fractional Exponent: a^m/n = ⁿ√(a^m)

Common Applications

• Compound Interest: A = P(1 + r)^t
• Population Growth: P(t) = P₀e^rt
• Radioactive Decay: N(t) = N₀e^-λt
• Computer Science: Binary operations (2ⁿ)
• Physics: Inverse square law (1/r²)