Integer Exponent
\(2^3 = 2 \times 2 \times 2 = 8\)
Exponential Calculator
Calculate powers aⁿ, including negative and fractional exponents, with a graph
Results
Enter values and click Calculate to see the result.
Theory & Formula
Exponentiation is a mathematical operation involving two numbers: the base (a) and the exponent (n).
Exponent rules and properties:
- Positive integer: aⁿ = a × a × ... × a (n times)
- Zero exponent: a⁰ = 1 (where a ≠ 0)
- Negative exponent: a⁻ⁿ = 1 / aⁿ
- Fractional exponent: a^(1/n) = ⁿ√a (nth root of a)
- Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ
- Power rule: (aᵐ)ⁿ = aᵐⁿ
\(y = a^n\)
Worked Examples
Negative Exponent
\(2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\)
Fractional Exponent
\(16^{1/2} = \sqrt{16} = 4\)