Power Calculator (bⁿ)
Raise any base to any exponent — whole, negative or fractional — and get the power, its reciprocal and scientific-notation form.
How it works
bⁿ = b · b · … (n factors) · Negative exponent b⁻ⁿ = 1 ÷ bⁿ · Fractional exponent b^(p ÷ q) = the q-th root of bᵖ
Raising a base to a power means repeated multiplication when the exponent is a whole number: 2¹⁰ is ten 2s multiplied together. The idea extends smoothly beyond counting — a negative exponent means take the reciprocal (b⁻ⁿ = 1 ÷ bⁿ), a fractional exponent means take a root (b^(1÷q) is the q-th root of b), and any base to the zero power is 1. A negative base only stays real when the exponent is a whole number, since fractional powers of negatives require complex numbers.
Worked example
For a base of 2 and exponent 10: 2¹⁰ = 2 × 2 × … × 2 (ten times) = 1024. Its reciprocal is 2⁻¹⁰ = 1 ÷ 1024 ≈ 0.0009766. As a check on fractional powers, 2^0.5 is the square root of 2 ≈ 1.4142, and 2⁰ = 1.
Sources: Exponentiation — Wikipedia
Frequently asked questions
What does a negative exponent mean?
It signals a reciprocal: b⁻ⁿ = 1 ÷ bⁿ. So 2⁻³ = 1 ÷ 2³ = 1 ÷ 8 = 0.125. The magnitude of the exponent still controls how many times you multiply; the sign just flips it into the denominator.
What is a fractional exponent?
A fractional exponent is a root. b^(1÷2) is the square root of b, b^(1÷3) is the cube root, and b^(p÷q) is the q-th root of bᵖ. This is why 9^0.5 = 3 and 8^(1÷3) = 2.
Why can’t I raise a negative base to a fractional power here?
Because there is no real answer: (−8)^(1÷2) would be the square root of a negative number, which lives in the complex plane. Negative bases are allowed only with whole-number exponents, where the sign is well defined.
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This calculator is for educational purposes. Double-check important results before acting on them.