Exponent Calculator
Calculate powers and exponents with step-by-step calculations. Supports positive, negative, and fractional exponents. Perfect for algebra, calculus, and scientific calculations.
Power Calculator
Common Exponent Examples
Click on these links to see instant calculations with common exponents:
Exponent Calculations
An exponent indicates how many times a base number is multiplied by itself. Exponents can be positive, negative, or fractional, each with specific rules and applications.
Exponent Rules and Properties
a^0 = 1 (any number to power 0 equals 1)
a^1 = a (any number to power 1 equals itself)
a^(-n) = 1/(a^n) (negative exponent rule)
a^(1/n) = ⁿ√a (fractional exponent as root)
a^(m/n) = ⁿ√(a^m) (general fractional exponent)
Common Exponent Examples
| Expression | Base | Exponent | Result |
|---|---|---|---|
| 2³ | 2 | 3 | 8 |
| 3² | 3 | 2 | 9 |
| 10² | 10 | 2 | 100 |
| 2⁻² | 2 | -2 | 0.25 |
| 4^0.5 | 4 | 0.5 | 2 |
- Mathematics: Solve exponential equations and power calculations
- Science: Calculate exponential growth, decay, and scientific notation
- Engineering: Power calculations, signal processing, and circuit analysis
- Finance: Compound interest and exponential growth models
- Computer Science: Algorithm complexity and binary operations
Frequently Asked Questions
What is an exponent?
An exponent is a number that indicates how many times a base number is multiplied by itself. In the expression a^n, 'a' is the base and 'n' is the exponent. For example, 2^3 = 2 × 2 × 2 = 8.
How do you calculate negative exponents?
A negative exponent means taking the reciprocal of the base raised to the positive exponent. For example, a^(-n) = 1/(a^n). So 2^(-3) = 1/(2^3) = 1/8 = 0.125.
What are fractional exponents?
Fractional exponents represent roots. a^(1/n) is the nth root of a, and a^(m/n) is the nth root of a raised to the mth power. For example, 8^(1/3) = ∛8 = 2, and 4^(3/2) = (√4)^3 = 2^3 = 8.