Exponent Calculator
Raise a base to an integer, negative, decimal, or fractional exponent and see the power, reciprocal, radical form, and calculation rule.
Exponent formulas
An exponent tells how a base is multiplied or transformed. The expression ab has base a and exponent b.
- For a positive integer n, an=a×a×…×a using n factors.
- For a nonzero base, a0=1.
- For a negative exponent, a−n=1/an.
- For a fractional exponent, am/n=ⁿ√(am) when the expression has a real value.
Checked examples
| Power | Rule | Result |
|---|---|---|
| 210 | Positive integer exponent | 1,024 |
| 50 | Zero exponent | 1 |
| 2−3 | 1/2³ | 0.125 |
| 91/2 | Square root | 3 |
| 272/3 | Cube root of 27² | 9 |
| (−8)1/3 | Real cube root | −2 |
| (−8)2/3 | Square of the cube root | 4 |
| (−2)4 | Even integer exponent | 16 |
| 4−1/2 | Reciprocal square root | 0.5 |
| 106 | Power of ten | 1,000,000 |
How to use the calculator
- Enter the base. Positive, negative, and zero bases are accepted where mathematically defined.
- Enter an integer, decimal, scientific-notation, or fractional exponent.
- Select Calculate power.
- Review the result and the matching reciprocal, radical, or multiplication form.
Limits and interpretation
- Base magnitude is limited to 1e100 and exponent magnitude to 10,000.
- Zero to the zeroth power is reported as indeterminate; zero to a negative exponent is undefined.
- Negative bases with non-integer exponents require an explicit reduced rational form with an odd denominator to produce a real result.
- Exact integer results are shown for manageable nonnegative integer powers; other results use approximately 14 significant digits.
- Results that overflow or underflow JavaScript double-precision arithmetic are rejected rather than displayed as infinity or zero.
- This tool returns real values only, not complex powers.
Frequently asked questions
What does a negative exponent mean?
It takes the reciprocal of the corresponding positive power. For example, 2−3=1/2³=1/8.
How do fractional exponents relate to roots?
The denominator gives the root and the numerator gives the power. Thus 272/3 is the cube root of 27 squared.
Why does a negative base sometimes have no real result?
An even root of a negative number is not real. Odd roots are real, so (−8)1/3=−2.
Is 00 equal to 1?
Different mathematical contexts use different conventions. This calculator reports 00 as indeterminate instead of silently choosing a convention.
Related calculators
Use the Logarithm Calculator to solve for an unknown exponent, the Square Root Calculator to simplify radicals, the Factorial Calculator for exact integer products, or the Scientific Notation Calculator for powers of ten.