Exponent Calculator

An exponent represents repeated multiplication of a base number. Understanding exponents is fundamental to algebra, calculus, and scientific calculations.

Exponent 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 (a ≠ 0)
• Negative Exponent: a^(-n) = 1/a^n

Special Cases

• Fractional Exponents: a^(1/n) = ⁿ√a
• Irrational Exponents: Use logarithms for calculation
• Complex Exponents: Require Euler's formula

Applications

• Compound Interest: A = P(1 + r)^t
• Population Growth: Exponential growth models
• Physics: Decay processes, wave functions
• Computer Science: Algorithm complexity, data structures
• Engineering: Signal processing, control systems

Common Powers

• 2^10 = 1,024 (kilobyte in binary)
• 10^3 = 1,000 (thousand)
• 10^6 = 1,000,000 (million)
• 10^9 = 1,000,000,000 (billion)