How this exponent calculator works
An exponent (also called a power or index) tells you how many times to multiply a base by itself. In the expression baseexponent, the base is the number being multiplied and the exponent is the number of factors. So 25 means "two multiplied by itself five times" — 2×2×2×2×2 = 32. This calculator computes the result instantly and, for small whole exponents, shows the full expanded multiplication.
The same idea extends beyond positive whole numbers. A negative exponent takes the reciprocal: b-n = 1 ÷ bn, so 5-2 = 1 ÷ 25 = 0.04. Zero as an exponent always gives 1 for a non-zero base (b0 = 1); the special case 00 is shown as 1 here by the common convention. A fractional exponent is a root: b1/n is the nth root of b, so 91/2 = √9 = 3. A negative base combined with a fractional exponent — such as (-8)1/2 — has no real value, and the tool flags this with a friendly note.
Powers of 2 reference
| Power | Value |
|---|---|
| 21 | 2 |
| 22 | 4 |
| 23 | 8 |
| 24 | 16 |
| 25 | 32 |
| 26 | 64 |
| 27 | 128 |
| 28 | 256 |
| 29 | 512 |
| 210 | 1,024 |
Reference note: results use standard floating-point arithmetic, so very large or fractional powers may be rounded. Values that exceed everyday magnitudes are shown in scientific notation (for example 1.0e+21).
Frequently asked questions
- What is an exponent?
- An exponent tells you how many times to multiply a base by itself. In base^exponent, the base is multiplied and the exponent is the number of factors — so 2^5 means 2×2×2×2×2 = 32.
- What is a negative exponent?
- A negative exponent means take the reciprocal of the positive power: b^-n = 1 ÷ b^n. For example, 5^-2 = 1 ÷ 25 = 0.04. The base must not be zero.
- What is anything to the power of 0?
- Any non-zero number to the power of 0 equals 1, since b^n ÷ b^n = 1. The case 0^0 is treated as 1 by convention here, though some contexts leave it undefined.
- What is a fractional exponent?
- A fractional exponent is a root: b^(1/n) is the nth root of b, so 9^(1/2) = √9 = 3 and 8^(1/3) = 2. A negative base with a fractional exponent, like (-8)^(1/2), is not a real number.
- How do I calculate powers?
- Multiply the base by itself as many times as the exponent says: 3^4 = 3×3×3×3 = 81. Use the reciprocal for negative exponents and the matching root for fractional ones — this tool does all of it automatically.
- What is 2 to the 10th power?
- 2^10 equals 1,024 — 2 multiplied by itself ten times. It is common in computing because 1,024 bytes make a kibibyte.