Exponent Calculator

Power: base ^ exponent

Root: the nth root of x

How it works

A power is repeated multiplication: 2¹⁰ = 2 × 2 × … × 2 (ten times) = 1,024. The rules extend naturally. A negative exponent flips the answer into a fraction: 2⁻³ = 1 ÷ 2³ = 0.125. A fractional exponent is a root: 9^(1/2) = √9 = 3, and 8^(2/3) means cube-root 8, then square it: 4. An exponent of 0 makes any non-zero base equal 1. The root tool runs the same math backwards, as x^(1/n).

Scientific notation writes a number as a mantissa times a power of ten — 5,120,000,000 as 5.12 × 10⁹ — so very large and very small results stay readable. The plain value above is shown in full whenever it fits comfortably (between 0.0001 and 10 quadrillion); beyond that, the scientific form is the headline.

Two cases are honestly impossible, and this page says so instead of guessing. Zero to a negative power would mean dividing by zero (0⁻² = 1 ÷ 0), which is undefined. And a negative base with a fractional exponent — like (−8)^(1/2) — has no answer among the real numbers (it needs imaginary numbers), so it is refused with an explanation. Note that (−8)^(1/3) is fine in the root tool, because odd roots of negatives exist: the cube root of −8 is −2. Zero to the power zero is reported as 1, the convention most calculators and programming languages use.

Worked example: 2¹⁰ = 1,024. And 5⁻² = 0.04, while the 4th root of 81 is 3.

Frequently asked questions

Why is anything to the power 0 equal to 1? Because dividing a power by its base steps the exponent down: 2³ ÷ 2 = 2², 2² ÷ 2 = 2¹, 2¹ ÷ 2 = 2⁰, and 2 ÷ 2 = 1 — so 2⁰ = 1, and the same pattern holds for every non-zero base.

What is the difference between (−2)² and −2²? Parentheses matter: (−2)² = (−2) × (−2) = 4, while −2² is read as −(2²) = −4. In this calculator the base is exactly what you type, sign included.

How big can the answer get? The math is done in double-precision floating point, exact for whole numbers up to about 9 × 10¹⁵ and meaningful to roughly 10³⁰⁸. Beyond that the result overflows and the page reports it instead of printing a wrong number.