Exponent Calculator
This exponent calculator raises any base to any power, and it handles the tricky ones: negative exponents, fractional exponents, and zero. Type a base and an exponent and you'll get the result, the expansion that shows where it comes from, the decimal and scientific notation, and the steps. There's a full exponent rules table below, so it teaches as well as solves.
- Any base and power
- Negative and fractional
- Shows the expansion
- Scientific notation
- Exponent rules
Last updated June 16, 2026 base to the power of the exponent Reviewed by the Calcowa math team
base ^ exponent
Try a negative exponent like −3, or a fractional one like 0.5 for a square root.
Enter a base and an exponent.
2⁵ = 2 × 2 × 2 × 2 × 2 = 32
What is an exponent?
An exponent tells you how many times to multiply a number by itself. In 2⁵, the 2 is the base and the small raised 5 is the exponent, so it means 2 × 2 × 2 × 2 × 2 = 32. People also call the exponent a power, and reading 2⁵ as "2 to the fifth power" means the same thing, so you won't get tripped by the two words. Exponents are a shorthand for repeated multiplication, which is why big numbers get big so fast, and you'll see that growth in the chart.
How to calculate an exponent
Here's the whole-number case, working out 2⁵:
- 1
Spot the base and exponentThe base is 2, the exponent is 5.
- 2
Multiply the base 5 times2 × 2 × 2 × 2 × 2.
- 3
Read the resultThat's 32, so 2⁵ = 32.
Negative and fractional exponents
A couple of cases trip people up, and they're worth a closer look. A negative exponent isn't a negative answer, it's a reciprocal: 2⁻³ means 1 ÷ 2³ = 1/8 = 0.125. A fractional exponent is a root: the power 1/2 is a square root, so 9^(1/2) = 3, and the power 1/3 is a cube root, so 27^(1/3) = 3. A fraction like 2/3 on top means you take the root and then raise to the power, and that's all there is to it. The calculator handles all of these and writes out what it did, so you don't have to second-guess the sign or the root.
Exponent rules
These rules let you combine and simplify powers without writing everything out, so you'll save a lot of steps. Here are the ones worth knowing.
| Rule | Formula | What it means |
|---|---|---|
| Product rule | xᵃ × xᵇ = xᵃ⁺ᵇ | Add exponents when multiplying same base |
| Quotient rule | xᵃ ÷ xᵇ = xᵃ⁻ᵇ | Subtract exponents when dividing |
| Power rule | (xᵃ)ᵇ = xᵃᵇ | Multiply exponents for a power of a power |
| Zero exponent | x⁰ = 1 | Any nonzero number to the 0 is 1 |
| Negative exponent | x⁻ⁿ = 1 / xⁿ | A negative power flips to a reciprocal |
| Fractional exponent | x^(1/n) = ⁿ√x | A unit fraction power is a root |
A fractional exponent ties straight into roots, so the fraction calculator helps when the power itself is a fraction.
Frequently asked questions
Is the exponent the same as the power?
Yes, the two words mean the same thing. The small raised number is the exponent, and "raised to the power of" is just how you say it out loud. So 2⁵, "2 to the fifth power", has an exponent of 5.
Multiply the base by itself as many times as the exponent says. So 2⁵ means 2 × 2 × 2 × 2 × 2 = 32, where 2 is the base and 5 is the exponent. The calculator shows this expansion for whole-number powers, and it'll work out the rest too.
A negative exponent means one over the positive power. So 2⁻³ is 1 ÷ 2³ = 1 ÷ 8 = 0.125. The base flips to the bottom of a fraction, and the exponent turns positive, so there's nothing scary about it. Enter a negative exponent above and you'll see it worked out.
A fractional exponent is a root. The power 1/n means the nth root, so 27^(1/3) is the cube root of 27, which is 3. A top number other than 1, like 8^(2/3), means take the root and then raise to that power, giving 4, so you've combined a root and a power in one step.
Any nonzero number raised to the power of 0 equals 1. It falls out of the exponent rules: x¹ ÷ x¹ is x⁰, and any number divided by itself is 1, so that's why x⁰ = 1. The one edge case, 0⁰, is usually taken as 1 by convention.
The main ones are: add exponents when multiplying the same base, subtract them when dividing, and multiply them for a power of a power. A zero exponent gives 1, a negative exponent gives a reciprocal, and a fractional exponent is a root. They're all listed in the table on this page.
The base is the number being multiplied, and the exponent is how many times. In 5³, the base is 5 and the exponent is 3, so it's 5 × 5 × 5 = 125. The exponent is written small and raised, which is why it's also called the power.
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