Exponent calculator
Work out xⁿ exactly for whole powers, and accurately for any other.
Result
Result: 1,024
- Exact value
- 1024
- Scientific notation
- 1.024 × 10³
- Number of digits
- 4
How it works
A whole-number exponent means repeated multiplication: 2⁵ = 2 × 2 × 2 × 2 × 2. A negative exponent means the reciprocal: 2⁻³ = 1/2³.
A fractional exponent is a root: x^0.5 is the square root of x. A negative base only has a real result when the root is odd, such as (−32)^0.2 = −2.
For whole exponents the calculator multiplies exactly with big integers, so 2^1000 is shown in full.
Formula
xⁿ = x × x × … × x (n times) x⁻ⁿ = 1 ÷ xⁿ x^(1/n) = ⁿ√x x⁰ = 1
Worked example
2¹⁰ = 1,024, which has 4 digits. 2⁻³ = 1/8 = 0.125. 10^0.5 ≈ 3.16227766, the square root of 10.
Questions people ask
Why is any number to the power 0 equal to 1?
Because xⁿ ÷ xⁿ = xⁿ⁻ⁿ = x⁰, and any non-zero number divided by itself is 1.
What does a negative exponent mean?
It means one divided by the positive power: 5⁻² = 1/25 = 0.04.
How big can the result be?
Whole-number powers are shown exactly up to tens of thousands of digits. Beyond that you get the value in scientific notation.