Exponent Calculator
Calculate powers and exponents with step-by-step solutions. Handle positive, negative, and fractional exponents with detailed explanations.
Calculator
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Quick Reference
• a⁰ = 1 (any number to power 0 equals 1)
• a¹ = a (any number to power 1 equals itself)
• a⁻ⁿ = 1/aⁿ (negative exponent)
• a^(1/2) = √a (fractional exponent)
How It Works
How Exponent Calculations Work
Exponents represent repeated multiplication. The base is multiplied by itself the number of times indicated by the exponent.
Basic Rules
- • a⁰ = 1 (any number to power 0 equals 1)
- • a¹ = a (any number to power 1 equals itself)
- • a⁻ⁿ = 1/aⁿ (negative exponent)
- • a^(1/2) = √a (fractional exponent)
Properties
- • aᵐ × aⁿ = a^(m+n)
- • aᵐ ÷ aⁿ = a^(m-n)
- • (aᵐ)ⁿ = a^(m×n)
- • (ab)ⁿ = aⁿ × bⁿ
Special Cases
Zero Exponent
Any non-zero number to the power of 0 equals 1
Negative Exponent
Negative exponents create reciprocals
Fractional Exponent
Fractional exponents represent roots
Examples
Exponent Calculation Examples
Positive Exponent
2³ = 2 × 2 × 2
Step 1: 2¹ = 2
Step 2: 2² = 4
Step 3: 2³ = 8
Result: 8
Negative Exponent
2⁻³ = 1/2³
Step 1: 2³ = 8
Step 2: 1/8 = 0.125
Result: 0.125
Fractional Exponent
9^(1/2) = √9
Fractional exponent means root
√9 = 3
Result: 3
Zero Exponent
5⁰ = 1
Any non-zero number to power 0
Always equals 1
Result: 1
Compare
Exponent Types Comparison
| Exponent Type | Example | Result | Meaning |
|---|---|---|---|
| Positive Integer | 2³ | 8 | Repeated multiplication |
| Zero | 5⁰ | 1 | Always equals 1 |
| Negative | 2⁻³ | 0.125 | Reciprocal |
| Fractional | 9^(1/2) | 3 | Root operation |
Common Applications
- • Scientific notation (10³ = 1,000)
- • Compound interest calculations
- • Population growth models
- • Computer science (2ⁿ for binary)
Calculation Tips
- • Use properties to simplify complex expressions
- • Convert negative exponents to fractions
- • Remember that x⁰ = 1 for any x ≠ 0
- • Use scientific notation for very large/small numbers
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