Raise any number to any power. Supports whole numbers, fractions, decimals, and negative exponents.
An exponent tells you how many times to multiply a base number by itself. In the expression 2³, the base is 2 and the exponent is 3, meaning 2 x 2 x 2 = 8. Exponents are fundamental to algebra, physics, computer science, and financial calculations. Special cases: any number to the power of 0 equals 1, and any number to the power of 1 equals itself.
Enter a base and an exponent (including negative exponents, fractions, and decimals). The calculator shows the result, the expanded multiplication form, and applies relevant exponent rules. It handles very large results and supports scientific notation for numbers that would otherwise be too long to display.
Product rule: a^m x 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) = nth root of a. The Logarithm Calculator solves the inverse: finding the exponent when you know the base and result.
Exponential relationships appear throughout nature, finance, and technology. Population growth follows exponential curves during unconstrained periods. Compound interest grows exponentially (which is why early investing has such outsized long-term impact). Sound intensity is measured in decibels, a logarithmic (inverse exponential) scale where every 10 dB increase represents a 10x increase in intensity. The Richter scale for earthquakes is also logarithmic: a magnitude 7 earthquake releases 31.6 times more energy than a magnitude 6. In computing, binary exponents define storage: 2^10 = 1,024 (approximately 1K), 2^20 = 1,048,576 (approximately 1M), 2^30 = approximately 1 billion (1G).