A classic power: 2¹⁰
- Input
- Base = 2, Exponent = 10
- Working
- 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Doubling step by step: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
- Result
- 2¹⁰ = 1024
Exponent Calculator
Raise any base to any power, including negative and fractional exponents, and see the repeated multiplication or root step that produces the answer. Runs entirely in your browser — your numbers never leave this device.
Calculation
Power
1,024
2^10 = 1,024
- Result
- 1,024
- Reciprocal (1 ÷ result)
- 0.0009765625
How it works
aⁿ = a × a × … × a (n times) | a⁰ = 1 (for a ≠ 0) | a^(−n) = 1 / aⁿ | a^(1/2) = √a | a^(m/n) = the n-th root of (a^m) | a^m × aⁿ = a^(m+n)
| Exponent (n) | 2ⁿ | Value |
|---|---|---|
| 0 | 2⁰ | 1 |
| 1 | 2¹ | 2 |
| 2 | 2² | 4 |
| 3 | 2³ | 8 |
| 4 | 2⁴ | 16 |
| 5 | 2⁵ | 32 |
| 6 | 2⁶ | 64 |
| 7 | 2⁷ | 128 |
| 8 | 2⁸ | 256 |
| 9 | 2⁹ | 512 |
| 10 | 2¹⁰ | 1,024 |
Enter a base and an exponent and the calculator raises the base to that power. For whole-number exponents the working spells out the repeated multiplication — 2¹⁰ is shown as ten 2s multiplied together — because that is what the notation means. The result is also given in scientific notation when it grows too large to read comfortably as a plain integer.
The exponent does not have to be a positive whole number, and the calculator follows the standard rules for the other cases. A zero exponent gives 1 for any non-zero base. A negative exponent gives the reciprocal: 2⁻³ = 1/2³ = 1/8 = 0.125. A fractional exponent is a root in disguise: the denominator becomes the root, so 16^(3/4) means take the fourth root of 16 (which is 2) and cube it, giving 8. The working names which rule was applied, so a surprising answer can be traced.
Two limits are handled honestly. Zero to the power zero (0⁰) is treated as undefined rather than silently returning 1, since mathematicians disagree on its value by context. And an even root of a negative base — such as (−16)^(1/2) — has no real answer, so the calculator reports that instead of returning an error code or a fake decimal. Very large powers may overflow into infinity in floating-point arithmetic, and when that happens the calculator says the result is too large to represent.
Worked examples
A negative exponent: 10⁻²
- Input
- Base = 10, Exponent = −2
- Working
- A negative exponent means take the reciprocal: 10⁻² = 1 / 10² = 1 / 100 = 0.01.
- Result
- 10⁻² = 0.01
A fractional exponent: 16^(3/4)
- Input
- Base = 16, Exponent = 3/4 = 0.75
- Working
- The denominator 4 is the root: the fourth root of 16 = 2, because 2⁴ = 16. The numerator 3 is the power: 2³ = 8.
- Result
- 16^(3/4) = 8
Frequently asked questions
Why is any number to the power 0 equal to 1?
Follow the pattern downwards: 2³ = 8, 2² = 4, 2¹ = 2 — each step divides by the base, so the next step, 2⁰, is 2 / 2 = 1. This holds for every non-zero base. The single exception is 0⁰ itself, which is left undefined because the patterns for zero and for exponents point to different answers.
What does a negative exponent do?
It flips the result into a reciprocal: a^(−n) = 1 / aⁿ. So 2⁻³ = 1/8 = 0.125 and 10⁻² = 0.01. The negative sign does not make the answer negative — 2⁻³ is positive 0.125. Only a negative base can produce a negative result.
What does a fractional exponent like 1/2 or 3/4 mean?
The denominator of the fraction is a root and the numerator is a power. Exponent 1/2 is the square root, so 9^(1/2) = 3. Exponent 3/4 on 16 means the fourth root of 16 (2) cubed, which is 8. You can apply the root first or the power first and get the same answer for positive bases.
When is the answer to a power negative?
Only when the base is negative and the exponent is an odd whole number: (−2)³ = −8, but (−2)² = +4 because the two negatives cancel. With an even root involved, a negative base has no real answer at all — (−16)^(1/2) would be the square root of −16, which is not a real number.
How are very large results shown?
In scientific notation once they outgrow a readable plain number: 2¹⁰⁰ is shown as approximately 1.27 × 10³⁰ rather than a 31-digit string. Calculations use double-precision floating point, accurate to about 15 significant digits, so the last digits of an enormous power are approximations, not exact digits.
Is my calculation uploaded or saved anywhere?
No. This exponent calculator runs 100% in your browser — the base and exponent you type are processed on your own device, nothing is uploaded, and no history is kept after you leave the page.
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