Exponent Calculator
Repeated Multiplication, Generalized
Raising a number to a power is shorthand for multiplying it by itself repeatedly, but the definition stretches well beyond whole-number exponents — negative exponents flip the base into a fraction, and fractional exponents become roots. This calculator evaluates base^exponent for any combination the math supports, and flags the one case it can't: a negative base raised to a non-integer exponent, which produces a complex number outside the scope of a real-number result.
The Formula
Integer exponents are computed as repeated multiplication; non-integer exponents use the standard power function. A negative base with a non-whole exponent is rejected rather than silently returning an incorrect real number.
Where Exponents Are Used
- Compound growth — compound interest, population growth, and radioactive decay all scale by a fixed base raised to a time-based exponent.
- Computer science — memory sizes, algorithmic complexity, and binary counting are built on powers of 2.
- Physical sciences — scientific notation and unit scaling (kilo-, mega-, giga-) rely on powers of ten.
- Geometry — area scales with the square of a linear dimension, volume with the cube.
| Base | Exponent | Result |
|---|---|---|
| 2 | 10 | 1,024 |
| 5 | −2 | 0.04 |
| 9 | 0.5 | 3 |
A fractional exponent of 0.5 is equivalent to a square root, which is why 9^0.5 equals √9 = 3.
How to Use This Calculator
- Enter the Base value.
- Enter the Exponent value.
- Select Calculate to see the result, rounded to six decimal places for non-integer outcomes.
Related Calculations
Working backward from a result to find the base? The Nth Root Calculator solves that direction. For the inverse operation of finding an exponent from a result, see the Logarithm Calculator.