Exponents & Powers Calculator
Compute base numbers raised to positive, negative, or fractional exponents. Handles scientific notation and large integer powers efficiently.
About
Exponentiation is a critical operation in fields ranging from computer science to physics. This calculator raises a base number to a specific power, supporting integer, decimal, negative, and fractional exponents. It is particularly robust for handling results that exceed standard display limits, utilizing scientific notation for readability. The tool correctly applies algebraic rules for negative exponents (reciprocals) and zero exponents (identity), ensuring valid results for edge cases where standard calculators might return errors or ambiguous values.
Formulas
The calculation is based on the definition of power.
For scientific notation, the result is normalized to the form:
Where m is the mantissa (1 ≤ |m| < 10) and n is the integer order of magnitude.
Reference Data
| Rule Name | Formula | Example |
|---|---|---|
| Product Rule | xa × xb = xa+b | 23 × 22 = 25 = 32 |
| Zero Exponent | x0 = 1 | 990 = 1 |
| Negative Exponent | x-n = 1xn | 2-2 = 0.25 |
| Fractional Exponent | x1/n = n√x | 40.5 = 2 |