🔺 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.