Power Calculator
Calculate the power of a number: aⁿ, including negative and fractional exponents.
Tip: Fractional exponents are roots: 8^(1/3) = ∛8 = 2, and 16^(0.5) = √16 = 4.
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About this digital tool
The power calculator raises a base to any exponent: positive, negative or fractional. Enter the base (a) and the exponent (n) and get aⁿ, together with the full expression. Any power with exponent 0 gives 1, and 0⁰ is taken as 1.
A positive power is repeated multiplication: 2¹⁰ = 1024. A negative exponent gives the reciprocal: 5⁻² = 1 ÷ 25 = 0.04. A fractional exponent is a root: 9^0.5 = √9 = 3. It is used in geometry (area, volume), in physics, in compound interest and in computer science, where powers of 2 matter (2¹⁰ = 1024 bytes in a kilobyte).
How to use
- Enter the base (a)
- Enter the exponent (n) — it can be negative or fractional
- See the result aⁿ
- See the calculation steps
- See the properties used
Frequently asked questions
What does a negative exponent mean?
A negative exponent means the reciprocal: a⁻ⁿ = 1/aⁿ. Example: 2⁻³ = 1/2³ = 1/8 = 0.125.
What is 0⁰?
Mathematically it is an indeterminate form, but by convention (especially in combinatorics and computer science) 0⁰ = 1.
What are the main properties of powers?
aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐˣⁿ; (ab)ⁿ = aⁿbⁿ; a⁰ = 1 (a≠0).
How do I calculate a power with a fractional exponent?
The exponent 1/n is the n-th root: 8^(1/3) = ∛8 = 2. For other fractions, raise to the power and take the root: 27^(2/3) = (∛27)² = 9.