The Rules of Exponents

Exponents compress repeated multiplication: 2¹⁰ = 1,024 means ten factors of 2. Key rules: x⁰ = 1, x⁻ⁿ = 1/xⁿ, xᵃ × xᵇ = x⁽ᵃ⁺ᵇ⁾, (xᵃ)ᵇ = xᵃᵇ, and fractional exponents are roots — 9^(1/2) = 3.

Exponential Growth Is Everywhere

Compound interest, population growth, and computing power all follow exponential laws. Because growth compounds, small differences in the exponent produce enormous differences in the result — 2¹⁰ is 1,024, while 2²⁰ is over a million.

Reading Big Numbers

Results beyond a few digits are hard to read, so this calculator also reports scientific notation (a × 10ᵇ). For negative exponents the reciprocal is shown: 2⁻³ = 1/8 = 0.125, useful when working with decay and probability.