🔺 Exponent Calculator
2^100 = 1,267,650,600,228,229,401,496,703,205,376 — every digit, where ordinary calculators overflow to 1.2676506e30. Negative and fractional exponents come out exact too.
Base: integer, decimal or fraction (3/2). Exponent: whole number (±10000) or a fraction like 1/3 for roots.
2^100 = 1,267,650,600,228,229,401,496,703,205,376
31
digits — every one exact
Every case exact: 2^100 with all 31 digits (calculators overflow to 1.267e30), 2^−3 = 1/8 (not 0.125…1), 54^(1/3) = 3∛2 (not 3.7798). Runs locally.
How the exponent calculator works
Three exponent cases, all exact. Whole-number exponents run on arbitrary-precision arithmetic — 2^100 produces all 31 digits, 2^1000 all 302, with the digit count stated. Negative exponents apply the reciprocal rule exactly: 2⁻³ is 1/8 the fraction, not 0.125 the float. Fractional exponents are roots: x^(p/k) is the k-th root of x^p, which the tool simplifies symbolically by extracting k-th-power factors — 54^(1/3) = ∛54 = 3∛2, with the factorization working shown. Bases can be integers, decimals or fractions ((3/2)³ = 27/8); a decimal approximation accompanies every non-integer result.
Exponentiation is where floating point fails loudest: doubles overflow at 2^1024, silently round above 2^53, and "3.7797631^3 ≈ 54" is the closest a decimal calculator gets to the exact statement ∛54 = 3∛2. It's also a reliable stumbling block for AI chatbots, which pattern-match large powers rather than computing them — a digits-exact answer is checkable in a way a confident paragraph is not.
Frequently asked questions
How large an exponent can it handle?
Whole-number exponents to ±10,000 — 2^10000 is a 3,011-digit integer, computed exactly (very large results state their digit count and show abbreviated digits). The limit is readability, not precision.
What does a negative exponent mean?
The reciprocal of the positive power: x⁻ⁿ = 1/xⁿ. So 2⁻³ = 1/8 and (3/2)⁻² = 4/9 — exact fractions here, where decimal calculators give 0.125 and 0.4444….
How do fractional exponents work?
x^(p/k) is the k-th root of x^p. The tool computes x^p exactly, then simplifies the k-th root symbolically: 54^(1/3) = ∛54 = 3∛2, because 54 = 27 × 2 = 3³ × 2. Enter the exponent as a fraction like 1/3 or 2/3.
Why does my calculator say 2^100 = 1.2676506e30?
It stores numbers as 64-bit floats with ~15–17 significant digits, so everything past that is discarded and shown in scientific notation. Exact integer arithmetic has no such ceiling — all 31 digits are real here.
Does it run locally?
Yes — BigInt and rational arithmetic in your browser, offline-capable.