Exponent Calculator
Calculate x raised to the power y, including negative and fractional exponents. Results update as you type.
Result
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Expression
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Scientific Notation
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Explanation
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How to Use the Exponent Calculator
- Enter the base (x): The number to be raised to a power.
- Enter the exponent (y): The power to raise the base to.
- View results: See the result, scientific notation, and step-by-step explanation.
Exponent Rules
| Rule | Formula | Example |
|---|---|---|
| Product Rule | xa × xb = xa+b | 23 × 24 = 27 = 128 |
| Quotient Rule | xa / xb = xa-b | 25 / 22 = 23 = 8 |
| Power Rule | (xa)b = xab | (23)2 = 26 = 64 |
| Zero Exponent | x0 = 1 | 50 = 1 |
| Negative Exponent | x-a = 1/xa | 2-3 = 1/8 = 0.125 |
| Fractional Exponent | x1/n = nth root of x | 81/3 = 2 |
Frequently Asked Questions
What is 0 raised to the power 0?
By convention, 00 is defined as 1 in most mathematical contexts, especially in combinatorics and algebra. This calculator follows that convention.
How do negative exponents work?
A negative exponent means taking the reciprocal. For example, 2-3 = 1/(23) = 1/8 = 0.125. The base is raised to the positive version of the exponent, then inverted.
What are fractional exponents?
A fractional exponent like xa/b means taking the bth root of x raised to the ath power. For example, 82/3 = (cube root of 8)2 = 22 = 4.