Free Exponent Calculator Online
This free online exponent calculator raises any base to any power and shows the result, scientific notation, and a step-by-step expansion. It handles positive, negative, zero, and fractional exponents.
The number to raise to a power
Supports positive, negative, zero, and fractional values
210 = ?
Result
2 raised to the power of 10
Step-by-step Expansion
210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1,024
Rules of Exponents
The Core Definition
xⁿ = x × x × ... × x (n times)
Exponentiation is repeated multiplication. The exponent calculator computes this for any real base and exponent, including edge cases like negative and fractional powers.
| Rule | Formula | Example |
|---|---|---|
| Product Rule | xᵃ · xᵇ = xᵃ⁺ᵇ | 2³ · 2⁴ = 2⁷ = 128 |
| Quotient Rule | xᵃ / xᵇ = xᵃ⁻ᵇ | 5⁶ / 5² = 5⁴ = 625 |
| Power of a Power | (xᵃ)ᵇ = xᵃᵇ | (2³)² = 2⁶ = 64 |
| Zero Exponent | x⁰ = 1 (x ≠ 0) | 7⁰ = 1 |
| Negative Exponent | x⁻ⁿ = 1/xⁿ | 2⁻³ = 1/8 = 0.125 |
| Fractional Exponent | x¹/ⁿ = ⁿ√x | 27¹/³ = ³√27 = 3 |
Worked Examples
Related Math Tools
Why Use This Free Exponent Calculator?
- Any base, any power
- Step-by-step expansion
- Scientific notation output
- Handles edge cases
- Always free, no ads
Where Exponents Show Up in Real Life
Compound Interest
The compound interest formula uses exponents: A = P(1 + r/n)ⁿᵗ. $10,000 at 5% compounded monthly for 10 years becomes $10,000 × (1.004167)¹²⁰ = $16,470. The exponent calculator can compute that power for you.
Computer Science
Binary numbers are based on powers of 2. A byte has 2⁸ = 256 possible values. A 32-bit integer holds up to 2³² = 4,294,967,296 values. Understanding exponents is fundamental to computing and data storage.
Science & Engineering
Scientific notation relies on powers of 10. The speed of light is 3 × 10⁸ m/s. Avogadro's number is 6.022 × 10²³. The exponent calculator converts between standard and scientific notation seamlessly.
Common Exponent Mistakes
These are the errors that trip up students and professionals alike when working with powers and indices.
Multiplying Instead of Exponentiating
2⁴ is not 2 × 4 = 8. It is 2 × 2 × 2 × 2 = 16. The exponent tells you how many times to multiply the base by itself, not by the exponent.
Distributing Exponents Over Addition
(a + b)² is not a² + b². It is a² + 2ab + b². Exponents distribute over multiplication, not addition. This is one of the most common algebra errors.
Negative Base Confusion
(-3)² = 9, but -3² = -9. Parentheses matter. Without them, only the 3 is squared, then the negative sign is applied. Always use parentheses when the base is negative.
Frequently Asked Questions
Disclaimer: This exponent calculator is for educational and informational purposes only. Results for extremely large exponents may be limited by floating-point precision.
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