Exponent Calculator
Raise any number to any power — including negative and fractional exponents — or find an nth root, with the working shown step by step.
Result
How It Works
An exponent says how many times a base number is multiplied by itself: 2^10 means 2 multiplied by itself 10 times, which is 1,024. A negative exponent means the reciprocal — 5^(−2) is 1 / (5 × 5) = 1/25 = 0.04. A fractional exponent means a root: 9^(1/2) is the square root of 9, which is 3, and 16^(1/4) is the fourth root of 16, which is 2.
An nth root is the reverse of a power: the cube root of 27 is 3 because 3 × 3 × 3 = 27. Roots of negative numbers only exist in the real numbers when the degree is odd — the cube root of −8 is −2, but the square root of −4 is not a real number.
Worked examples: 2^10 = 1,024. 5^(−2) = 1/25 = 0.04. 9^(1/2) = 3. Cube root of 27 = 3 (3 × 3 × 3 = 27). Fourth root of 16 = 2 (2 × 2 × 2 × 2 = 16).
How to Use This Calculator
Pick a mode from the dropdown, enter the numbers, and the answer updates live with the working shown underneath.
- Power (a^b) — enter a base and any exponent, including negative or fractional ones. Try 2 and 10 for 1,024, or 5 and −2 for 0.04.
- Nth root (ⁿ√x) — enter a number and a whole-number degree of 2 or more. Try 27 and 3 for the cube root, 3.
- Read the check line — for roots with a whole-number answer, the calculator shows the multiplication that proves it.
The Reset button restores the examples so you can start over.
Tips and Practical Advice
Exponents turn up in compound interest, computer storage (1 KB = 2^10 bytes), science and everyday growth calculations — and small exponent slips cause big errors, so it pays to be careful.
- Anything to the power 0 is 1. 7^0 = 1 and 1,000^0 = 1 — the only exception is 0^0, which mathematicians leave undefined.
- Watch the minus sign. (−2)^2 = 4, but −2^2 = −4: brackets decide whether the minus is part of the base. In this calculator, enter the base as −2 to include it.
- Use fractional exponents for roots. Instead of hunting for a root button, remember that x^(1/n) is the nth root of x — 16^(1/4) = 2 is the same as the fourth root of 16.
- Check huge answers for sense. Powers grow fast — 2^30 is already over a billion — so if a result looks wildly large, re-read the exponent you typed.
Frequently Asked Questions
What does a negative exponent mean?
It means the reciprocal: a^(−n) = 1 / a^n. So 5^(−2) = 1 / 25 = 0.04.
What does a fractional exponent mean?
A fractional exponent means a root: a^(1/n) is the nth root of a. 9^(1/2) = 3 (square root) and 27^(1/3) = 3 (cube root).
Can you take a root of a negative number?
Only with an odd degree: the cube root of −8 is −2. An even root of a negative number, like the square root of −4, is not a real number.
What is 2 to the power of 10?
2^10 = 1,024. This is why computers use 1,024 as the step between KB, MB and GB in binary units.
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