Free online exponent calculator
An exponent tells you how many times to multiply a base number by itself. This calculator handles any base and exponent, including roots (fractional exponents) and negative powers.
Result
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How to use
- Enter a base number.
- Enter an exponent (can be negative or fractional).
- Click Calculate or press Enter.
- See the result and scientific notation.
Formula
b^n = b × b × b × … (n times)
For non-integer exponents: b^(p/q) = q-th root of b^p
Key rules
| Expression | Result |
|---|---|
| b^0 | 1 (any non-zero b) |
| b^1 | b |
| b^(−n) | 1/b^n |
| b^(1/2) | √b (square root) |
| b^(1/3) | ∛b (cube root) |
| b^(m/n) | n-th root of b^m |
Worked examples
| Expression | Result |
|---|---|
| 2^10 | 1,024 |
| 10^6 | 1,000,000 |
| 9^0.5 | 3 |
| 2^(−3) | 0.125 |
| 10^20 | 1 × 10^20 |
Frequently asked
What is an exponent?
An exponent (or power) tells how many times to multiply the base by itself. For b^n, b is the base and n is the exponent. 2^3 = 2 × 2 × 2 = 8.
What does a negative exponent mean?
A negative exponent means take the reciprocal: b^(−n) = 1/b^n. So 2^(−3) = 1/8 = 0.125.
How do fractional exponents work?
A fractional exponent represents a root: b^(1/n) is the nth root of b. So 9^(1/2) = √9 = 3, and 27^(1/3) = ∛27 = 3.
What is b^0?
Any non-zero number raised to the power of 0 equals 1. This is a fundamental rule — 5^0 = 1, 100^0 = 1.
What happens with a negative base and fractional exponent?
A negative base with a fractional exponent produces a complex (imaginary) number — for example, (−4)^0.5 = √(−4), which is imaginary. The calculator returns an error in this case.