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Exponent / Power Calculator

Calculate any base raised to any exponent. Supports negative exponents, fractional powers, and scientific notation output.

Calculate bn

bn

How to Use This Tool

  1. Choose a mode: Power (bⁿ), Scientific Notation, or Powers Table.
  2. For Power mode, enter the base and the exponent to instantly calculate the result.
  3. Check the scientific notation badge that appears when the result is very large or very small.
  4. For Scientific Notation mode, enter any number to convert it into coefficient × power-of-10 form.
  5. For Powers Table mode, enter a base to see a table of its powers from exponent 0 through 11.

Formula & How It Works

Integer Exponent

bⁿ = b × b × ... × b (n times)

Raising a base b to a positive integer exponent n means multiplying b by itself n times.

Negative Exponent

b⁻ⁿ = 1 / bⁿ

A negative exponent means take the reciprocal of the base raised to the positive exponent.

Fractional Exponent (Root)

b^(1/n) = ⁿ√b

A fractional exponent of 1/n represents the nth root of the base.

Scientific Notation

N = c × 10^e, where 1 ≤ c < 10

Any number can be written as a coefficient between 1 and 10 multiplied by a power of 10.

Practical Examples & Common Use Cases

Example: 2¹⁰

2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024.

Example: 2⁻³

2⁻³ = 1 / 2³ = 1 / 8 = 0.125.

Example: 450,000 in scientific notation

450,000 = 4.5 × 10⁵, since moving the decimal point 5 places gives a coefficient of 4.5.

Frequently Asked Questions

An exponent (or power) indicates how many times to multiply a base number by itself. In b^n, b is the base and n is the exponent. Example: 3^4 = 3 × 3 × 3 × 3 = 81.

A negative exponent means take the reciprocal. b^-n = 1 / b^n. For example, 2^-3 = 1/8 = 0.125.

A fractional exponent represents a root. b^(1/n) is the nth root of b. For example, 27^(1/3) = ∛27 = 3.

Scientific notation writes very large or very small numbers as a coefficient (between 1 and 10) multiplied by a power of 10. Example: 450,000 = 4.5 × 10^5.

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