About the Exponent Calculator
Exponent Calculator does four related jobs. Power raises a base to an exponent, and when both are whole numbers it shows the exact integer, up to 300 digits, as well as the scientific form. Root finds the nth root of a number, such as the cube root of 27. Logarithm gives the log of a number in any base, with quick buttons for base 10, 2 and e, and shows ln and log10 as well. Square root gives the value and, for whole numbers, the simplified radical, such as √72 = 6√2. Each result has a short explanation in words and a copy button. Decimal results are ordinary floating-point numbers with about 15 to 16 significant digits, and complex numbers are not supported, so an even root of a negative number has no answer here.
Updated October 2026
How to use the Exponent Calculator
- 1Choose Power, Root, Logarithm or Square root.
- 2Type the numbers in the boxes, such as base 2 and exponent 10.
- 3For a logarithm, pick the base with the 10, 2 or e buttons, or type your own.
- 4Read the result, the working in words and any extra values.
- 5Tap Copy result to use the answer elsewhere.
Exponent rules in short
- Same base, multiply: x^a × x^b = x^(a+b).
- Same base, divide: x^a ÷ x^b = x^(a−b).
- Power of a power: (x^a)^b = x^(a×b).
- Zero exponent: x^0 = 1 for any x other than 0.
- Negative exponent: x^(−a) = 1 ÷ x^a.
Roots as fractional exponents
The nth root of x is the same as x raised to the power 1/n. The square root is the power 1/2 and the cube root is the power 1/3. That is why 9 to the power 0.5 equals 3.
Roots of negative numbers work only for odd n, because a negative times itself an odd number of times stays negative. For a square root you can also see the simplified radical: √72 becomes 6√2, since 72 is 36 × 2 and 36 is a perfect square.
Logarithms: the reverse of powers
If 2 to the power 3 is 8, then the log base 2 of 8 is 3. Logarithms turn multiplication into addition, which is why they were used for slide rules and are still used for decibels, pH and the Richter scale.
The tool computes log base b of x as ln(x) divided by ln(b), and snaps answers that are within a hair of a whole number, so log base 10 of 1,000 shows exactly 3. For general arithmetic beyond these four functions, use Online Calculator.
Big numbers and scientific notation
Powers grow quickly. Two to the power 100 has 31 digits, and the calculator shows all of them when both numbers are whole and the result is under 300 digits. Beyond about 15 digits it also gives scientific notation, such as 1.2677e+30.
Ordinary decimal results are limited by floating-point precision, which is about 15 to 16 significant digits. If you need to check a fraction result, Fraction Calculator keeps it exact. For other base work, use the Number Base Converter, and use the Percentage Calculator for growth rates.
Features
- Exact integer powers up to 300 digits
- Scientific notation for very large or small results
- Nth roots, including odd roots of negative numbers
- Logarithms in any base, with ln and log10
- Simplified radical form for square roots
- Plain-words explanation with every result
- Runs in your browser
Frequently asked questions
What is an exponent?
An exponent tells how many times a number, the base, is multiplied by itself. In 2 to the power of 10, the base 2 is used 10 times, so the result is 1,024. Negative exponents give fractions, and fractional exponents give roots.
What is anything to the power of 0?
Any number other than zero raised to the power 0 is 1. The calculator also gives 1 for 0 to the power 0, which is the usual convention in algebra and computing, although some textbooks leave that case undefined.
How do I calculate a negative exponent?
Take the reciprocal and make the exponent positive. Two to the power of −2 is 1 divided by 2 squared, which is 0.25. The explanation under the result writes this out for your numbers.
How do I find the cube root of a number?
Choose Root, type the number and set the root to 3. The cube root of 27 is 3 because 3 × 3 × 3 is 27. Odd roots also work for negative numbers, so the cube root of −27 is −3.
What is a logarithm?
A logarithm answers the question: to what power must the base be raised to get this number? The log base 10 of 1,000 is 3, because 10 to the power 3 is 1,000. Base 10, base 2 and base e (the natural log, ln) are the most common.
Why does my calculator say a negative root doesn't exist?
An even root, such as a square root or fourth root, of a negative number is not a real number, because no real number multiplied by itself an even number of times gives a negative result. It exists as a complex number, which this tool does not calculate.