Math Calculators
Exponent Calculator
A power is repeated multiplication: 2^10 means ten copies of 2 multiplied together. A root asks the opposite question — which number, multiplied by itself n times, gives this value. Enter either direction, and this page returns the answer exactly when the mathematics is exact, marking it as rounded when it is not.
Calculator
Formula
The whole page rests on one definition. For a positive integer exponent, aⁿ is a multiplied by itself n times: aⁿ = a × a × … × a, with n factors. A root is the same statement read backwards and it is defined that way: ⁿ√x is the number whose nth power is x, which is exactly x raised to the power 1/n. Everything else follows from those two sentences. a⁰ = 1 for any nonzero a, because aᵐ ÷ aᵐ = 1 and the quotient rule makes that a⁰. A negative exponent is a fraction rather than a sign, because a⁻ⁿ is defined as 1 ÷ aⁿ — the only reading that keeps aⁿ × a⁻ⁿ = 1 true. Three things are stated rather than left to the reader. 0⁰ is refused as indeterminate, because 0⁰ = 1 is a convention of particular fields and not the mathematics of the expression. A result is exact when its exact decimal terminates inside the double's own window — an integer at or below 9007199254740991, or a fraction of at most fifteen significant digits — and it is then printed in full. Anything else is rounded to eight significant digits and marked as rounded: 1.1² prints 1.21, never the 1.2100000000000002 a chain of double multiplications produces.
About This Calculator
What It Does
This page answers one relation — aⁿ = b — read in whichever direction you asked for. In power mode it raises a base to an exponent; in root mode it takes the nth root of a radicand. The two are not separate calculations: a root is defined as the exponent 1/n, so the page computes one power and reads it from the side you named. Under the result sits a fixed table of the eight exponent rules and the notation they are written in.
Worked Example
The page opens in power mode with a base of 2 and an exponent of 10, and computes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024, printed exactly because 1024 is a whole number inside the range the page prints in full. Switch Find to Root, leave the radicand at 8 and the index at 3, and the page answers 2 — exactly, because 2 × 2 × 2 = 8, so ⁿ√8 with n = 3 is the number whose cube is 8.
Real-World Usage
Use it to work out compound growth over a number of periods, to scale an area or a volume when one dimension changes, to read a magnitude written as a power of ten, or to check a power of two when you are sizing memory or a disk. It is also the page to reach for when a number in a document is written with a negative or fractional exponent and you want the plain value.
Local Context
Exponentiation is a property of the numbers and not of the country, so nothing here changes with your location and the page serves one set of answers everywhere — the arithmetic is consolidated to a single page per language. Two conventions are worth knowing. The decimal separator in the input fields is the point, as in 1.5 and 0.125, whatever separator your language uses in ordinary prose; the result is formatted in your language's own convention, so the same answer reads 1,5 in German and 1.5 in English. And an exact answer is printed in full, while a rounded one is marked as rounded next to its eight-significant-digit value.
Sources and Methodology
The eight exponent rules on this page are the standard algebraic identities that follow from repeated multiplication, and each row's derivation is stated in the calculator module itself. The convention around zero to the power of zero was read from the English-language Wikipedia article “Zero to the power of zero” (October 2026), which records both the fields that define 0⁰ as 1 and the argument that the expression is undefined. The exactness window and the eight-significant-figure display rule are this page's own and are stated on it, not quoted from a standard.
Last reviewed: October 2026.
Frequently Asked Questions
Why does 2^10 print 1024 and not 1024.0000000000001?
Because the two are not the same answer. 2^10 is a whole number, and this page computes a whole-number result with exact integer arithmetic, so it prints every digit of it. Many calculators evaluate a power through logarithms or a chain of floating-point multiplications, which is why they show a stray digit at the end — 1.1² reads 1.2100000000000002 that way. This page takes the same value and answers 1.21.
Why is 0^0 refused instead of shown as 1?
Because there is no agreement about it, and the page will not pretend otherwise. In some fields 0⁰ is defined as 1 — it is what makes the binomial theorem and the empty product work — while the expression has no limit at that point, and every nearby path gives a different value. Programming languages settle the question one way for convenience: JavaScript's Math.pow(0, 0) is 1. This page names the disagreement instead of taking a side. Every other base behaves as usual: a⁰ = 1 for any nonzero a.
Why does a negative exponent give a fraction?
Because that is what makes the rules consistent. The product rule says aⁿ × a⁻ⁿ = a⁰ = 1, so a⁻ⁿ has to be whatever multiplies aⁿ to give 1 — and that is 1 ÷ aⁿ. It is a definition, chosen to keep the algebra true, not a rule about signs: 2⁻³ = 1 ÷ 8 = 0.125, a positive number. The page prints that value exactly rather than rounding it.
Why can I not take the square root of a negative number?
Because no real number multiplied by itself gives a negative result: a negative times a negative is positive. So an even root of a negative radicand is refused as not real. An odd index is different, and it is allowed here: −2 multiplied by itself three times is −8, so the cube root of −8 is exactly −2, and the page says so rather than approximating it.
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