Exponent Calculator
Calculate base numbers raised to integer, negative, and fractional powers with scientific notation formatting.
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How to Use the Exponent Calculator – Powers & Scientific Notation
- 1Enter the base number (b) into the first box.
- 2Enter the exponent or power (n) into the second box.
- 3Read the calculated result in standard decimal and scientific notation.
- 4Review the power rule explanations and step-by-step breakdown.
Formula & How It Works
Exponentiation Rules & Laws of Powers
Exponentiation bⁿ represents multiplying base b by itself n times for positive integers. For negative exponents, b⁻ⁿ = 1 / bⁿ. For zero exponents, b⁰ = 1 (where b ≠ 0). For fractional exponents, b^(m/n) represents the n-th root of b raised to power m.
Worked Examples
Standard Cube Power
Input: Base: 5, Exponent: 3
Explanation: 5 raised to the 3rd power equals 5 × 5 × 5 = 125.
Negative Exponent Division
Input: Base: 2, Exponent: -3
Explanation: 2⁻³ = 1 / (2³) = 1 / 8 = 0.125.
Computer Science Power of Two
Input: Base: 2, Exponent: 16
Explanation: 2¹⁶ represents the maximum value range of a 16-bit integer.
Fractional Exponent (Square Root)
Input: Base: 81, Exponent: 0.5 (1/2)
Explanation: Raising a number to the 0.5 power is mathematically identical to taking its square root: √81 = 9.
Frequently Asked Questions
What does a negative exponent mean?▼
A negative exponent means taking the reciprocal of the base raised to the positive power: b⁻ⁿ = 1 / bⁿ (e.g. 10⁻² = 1/100 = 0.01).
Why does any non-zero number to the power of 0 equal 1?▼
According to exponent division laws, bⁿ / bⁿ = b^(n - n) = b⁰. Since any number divided by itself equals 1, b⁰ must equal 1.
What is 0 to the power of 0?▼
In mathematics, 0⁰ is generally treated as an indeterminate form in calculus, though defined as 1 in discrete algebra and combinatorics.
How large of a power can this calculator handle?▼
The tool handles numbers up to JavaScript's Number.MAX_VALUE (~1.8 × 10³⁰⁸) and switches to scientific notation for large results.
Can I enter decimal bases and exponents?▼
Yes, you can calculate fractional powers such as 2.5^1.75.
Does this tool work completely offline?▼
Yes, all exponential arithmetic runs locally in your web browser with zero server latency.
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