Exponent Calculator

Compute powers, roots, e^x and ln(x) with exact integers where possible, scientific notation, and honest notes on overflow, 0^0 and complex results.

All powers and roots are computed locally in your browser. Nothing ever leaves your device.

Value
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Scientific notation
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Order of magnitude
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Exponent rules cheat sheet
aᵐ · aⁿ = aᵐ⁺ⁿ   2³ · 2⁴ = 2⁷ = 128
aᵐ ÷ aⁿ = aᵐ⁻ⁿ   5⁶ ÷ 5² = 5⁴ = 625
(aᵐ)ⁿ = aᵐⁿ   (3²)³ = 3⁶ = 729
a⁻ⁿ = 1 ÷ aⁿ   2⁻³ = 1/8 = 0.125
a^(m/n) = ⁿ√(aᵐ)   8^(2/3) = (∛8)² = 4
a⁰ = 1 (a ≠ 0)   99⁰ = 1

How It Works

Powers with whole exponents are multiplied out exactly — integers are computed with BigInt when they fit within JavaScript's 2^53 exact-integer window or when the base and exponent are both integers, so results like 2^100 come out digit-perfect. Everything else (fractional, decimal, or irrational exponents) goes through the identity a^b = e^(b·ln a), which is also how your calculator chip and every programming language evaluate powers, and that is where the 16-digit float limit comes from.

Fractional exponents are roots
a^(m/n) means the n-th root of a^m, and the two readings agree: 8^(2/3) = (∛8)² = 2² = 4, and equally (8²)^(1/3) = ∛64 = 4. The calculator accepts exponents typed as fractions like 2/3 so the root form is exact rather than the float 0.6666666666666666.
Negative exponents are reciprocals
a^(-n) = 1 ÷ aⁿ — a minus sign on the exponent never flips the value's sign, it only moves it to the other side of a division: 2⁻³ = 1/8. The Steps panel prints that reciprocal line whenever the exponent is negative, and for root mode it shows the equivalent fractional power, since ⁿ√x = x^(1/n).
Floating-point limits, stated honestly
IEEE-754 doubles top out at about ±1.8 × 10^308 and bottom out near 10^(-308) before underflowing to zero, with roughly 16 significant digits in between. Results beyond the ceiling are reported as overflowing the double limit instead of collapsing to Infinity silently, and 0^0 is answered with the convention discussion rather than a bare number.

Frequently Asked Questions

How is 2^100 shown without losing precision?

As an exact integer when JavaScript can hold one. Doubles store integers exactly up to 2^53, so 2^100 is computed digit-by-digit with BigInt and printed in full: 1267650600228229401496703205376. The scientific-notation and order-of-magnitude cards always accompany it, because 1.267650600 × 10^30 is the form that is readable at a glance.

Why does the calculator not just answer 1 for 0^0?

Because mathematicians genuinely disagree, so the tool stays honest. Combinatorics defines 0^0 = 1 because it counts empty products and empty functions. Analysis leaves it undefined because the limit of x^y depends on the path taken toward (0, 0) — x^0 tends to 1 while 0^x tends to 0. This calculator prints the convention note instead of silently picking a side.

What about (-8)^(1/3)? JavaScript's pow() says NaN.

The real cube root of -8 is -2, and this calculator returns it: when the exponent is a fraction p/q in lowest terms with an odd q, the root exists and is computed as sign-aware cbrt (or Math.cbrt(a)^p). For decimal exponents you enter, the same reduction to a fraction is attempted. Non-integer powers of negative numbers whose fractional form has an even denominator — like (-8)^0.5 — land in the complex plane and are reported as out of scope rather than printed as NaN.

Why do some results end in tiny rounding errors?

Every non-integer power is evaluated with floating-point logarithms, and doubles only carry about 16 decimal digits. 1.1^100 shows as 13780.612339822... not because the algorithm is sloppy but because that is the limit of binary representation. When the true answer is an integer — like 2^10 or 8^(2/3) — the calculator detects and prints the exact value instead.

Is anything uploaded to a server?

No. Powers, roots, exponentials and logarithms are computed locally in your browser with JavaScript's Math functions and BigInt. Your numbers never leave your device, and there is no account, tracking or network request attached to a calculation.