Formula
bⁿ = b × b × … × b (n times)b⁻ⁿ = 1 ÷ bⁿb^(1/n) = the n-th root of b
- b⁰ = 1 for any non-zero b
- A negative base needs a whole-number exponent to give a real result
Multiply the base by itself as many times as the exponent says.
Worked examples
2 to the power of 10
- Base
- 2
- Exponent
- 10
Result
1,024
Exact integer: 1,024
Scientific notation: 1.024 × 10³
2 to the power of −3
- Base
- 2
- Exponent
- −3
Result
0.125
As a fraction: 1 / 8
Scientific notation: 1.25 × 10⁻¹
How it works
An exponent says how many times to multiply the base by itself: 2¹⁰ = 1,024. A zero exponent gives 1, a negative exponent gives a reciprocal (2⁻³ = 1 ÷ 8 = 0.125) and a fractional exponent is a root, so 9^0.5 is the square root of 9.
For whole-number bases and exponents the calculator uses exact integer arithmetic, so 7²⁵ is shown with every digit instead of a rounded decimal, and a negative power of a whole number also shows its exact fraction. Other results are shown to about 12 significant digits, with scientific notation for very large or small values.
A negative base raised to a fractional power has no real value, and zero cannot be raised to a negative power because that means dividing by zero; the tool explains either case instead of returning an error. For roots use the Square Root Calculator, for the inverse operation the Logarithm Calculator, and for growth over time the Compound Interest Calculator.
Assumptions and limits
- 0⁰ is taken as 1, the usual calculator convention.
- Exact digits are shown for whole-number bases up to 10⁹ and exponents up to 2,000 when the result has at most 400 digits.