Calculating power...
Enter a base and exponent to see the result
The result will show the decimal answer, scientific notation, steps, and a magnitude chart.
Exponent rules
How the exponent calculator works
An exponent calculator evaluates expressions like a^n, where the base is multiplied by itself according to the exponent. This power calculator also handles negative exponent, fractional exponent, and nth root inputs so you can move between powers and radicals without rewriting everything by hand.
Positive powers
2^4 means repeated multiplication: 2 × 2 × 2 × 2 = 16.
Negative exponents
2^-3 becomes the reciprocal 1 / 2^3 = 0.125.
Fractional exponents
81^(3/4) means take the fourth root, then raise the result to the third power.
Repeated multiplication diagram
A whole-number exponent counts how many copies of the base are multiplied.
Negative exponent diagram
A negative exponent moves the power to the denominator.
Fractional exponents and nth roots
A fractional exponent combines a root and a power. The denominator tells you the root index; the numerator tells you the power. That is why a^(1/2) is a square root and a^(1/3) is a cube root.
The calculator checks the real-number domain before returning an answer. For example, the cube root of -8 is real, but the square root of -8 is not real.
Common exponent examples
| Expression | Meaning | Result |
|---|---|---|
| 2^10 | 2 multiplied 10 times | 1024 |
| 5^-3 | 1 / 5^3 | 0.008 |
| 16^(1/2) | Square root of 16 | 4 |
| 27^(1/3) | Cube root of 27 | 3 |
Related math tools
FAQ
What does a negative exponent mean?
A negative exponent means reciprocal. For example, a^-3 equals 1 / a^3 when a is not zero.
What does a fractional exponent mean?
A fractional exponent a^(p/q) means the qth root of a raised to the p power.
Can this exponent calculator handle negative bases?
Yes, when the real-number result exists. Integer exponents and fractions with odd denominators can work; even roots of negative numbers are not real.
External references