Exponent Calculator

Mathematics

Calculate base numbers raised to positive, negative, and fractional powers (xʸ). Evaluate exponential growth, power laws, and reciprocal powers instantly.

Calculated Result
1,024
Formula: aᵇ

About this calculator

Exponents describe natural phenomena characterized by rapid multiplication or radioactive decay, from bacterial population growth and compound interest to acoustic decibels and seismology.

This calculator handles integer exponents, negative powers (which represent reciprocals: x⁻ⁿ = 1/xⁿ), and fractional exponents (which represent radical roots: x^(m/n) = ⁿ√(xᵐ)).

How It Works & Formula

Formulaaᵇ for real a, b (negative bases only with integer b)

For positive real bases, evaluation uses base-e exponential transformation xʸ = exp(y × ln(x)). For negative integer bases, signs flip based on whether the exponent is even or odd.