Exponent calculator
Enter a base and an exponent and get aˣ straight away. Negative exponents, fractional exponents (roots) and very large results work too.
Decimals may use a point or a comma. A sum works too, such as 2^10 or sqrt(2).
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
Rules for powers
- a⁰ = 1 (for a ≠ 0)
- a⁻ⁿ = 1 ÷ aⁿ, so 2⁻³ = 1/8 = 0.125
- a^(1/n) is the n-th root, so 27^(1/3) = 3
- aᵐ · aⁿ = aᵐ⁺ⁿ and (aᵐ)ⁿ = aᵐⁿ
What doesn't work?
0 to a negative power would mean dividing by 0, and a negative base with a fractional exponent, such as (−8)^0.5, has no real answer. The calculator tells you instead of giving NaN. Very large or small answers are also shown in scientific notation. For growth over time, use the exponential growth calculator.
Examples
| Base | Exponent | Result |
|---|---|---|
| 2 | 10 | 1,024 |
| 2 | −3 | 0.125 |
| 9 | 0.5 | 3 |
| 27 | 1/3 | 3 |
| 10 | 6 | 1,000,000 |
| 1.05 | 10 | 1.6289 |
The exponent field accepts sums like 1/3, so you do not have to type 0.3333.
A negative base
(−2)² = 4, because the base −2 is multiplied by itself. Enter −2 as the base and 2 as the exponent to see it. Writing −2² on paper means −(2²) = −4, since the power binds tighter than the minus sign, which is a common source of mistakes.
Compound growth
A power with a base like 1.05 is how percentages build up: 1.05¹⁰ ≈ 1.6289 means 62.9% growth after ten years of 5%. The exponential growth calculator turns that into an end value and a doubling time. The inverse of a power is a logarithm: for 2ˣ = 50, use the logarithm calculator.
Frequently asked questions
How do I calculate a square root or cube root here?
Use a fractional exponent. A square root is the power 0.5 (or 1/2): 9^0.5 = 3. A cube root is the power 1/3: 27^(1/3) = 3.
Why is a negative exponent a fraction?
Because a⁻ⁿ is defined as 1 ÷ aⁿ. That keeps the rule aᵐ · aⁿ = aᵐ⁺ⁿ true: 2⁵ · 2⁻³ = 2², and 32 ÷ 8 = 4.
How do I take the cube root of a negative number?
The calculator refuses a negative base with a fractional exponent. Take the root of the positive number and put the sign back: the cube root of −8 is −(8^(1/3)) = −2.
What happens with huge results like 2^100?
They are shown in scientific notation, here about 1.27 × 10³⁰, instead of a number with thirty digits.