Exponent Calculator
Calculate exponents and powers. Learn exponent rules, scientific notation, and how to solve exponential equations.
Calculate Power
Exponent Result
0
2^10
0
standard form
💡 Remember: x^n means multiplying x by itself n times. For example, 2^3 = 2 × 2 × 2 = 8.
What is an Exponent?
An exponent (also called a power or index) indicates how many times a number (the base) is multiplied by itself. It is written as a small number to the upper right of the base.
Basic Exponent Rules
| Rule | Formula | Example |
|---|---|---|
| Product Rule | a^m × a^n = a^(m+n) | 2^3 × 2^4 = 2^7 = 128 |
| Quotient Rule | a^m ÷ a^n = a^(m-n) | 5^6 ÷ 5^2 = 5^4 = 625 |
| Power Rule | (a^m)^n = a^(m×n) | (3^2)^3 = 3^6 = 729 |
| Zero Exponent | a^0 = 1 (a ≠ 0) | 7^0 = 1 |
| Negative Exponent | a^(-n) = 1/a^n | 2^(-3) = 1/8 = 0.125 |
| Fractional Exponent | a^(1/n) = ⁿ√a | 8^(1/3) = 2 |
Special Cases
- Base of 0: 0^n = 0 (for n > 0). 0^0 is undefined.
- Base of 1: 1^n = 1 for any n.
- Exponent of 1: a^1 = a.
- Exponent of 2: Called "squared" (e.g., 5² = 25).
- Exponent of 3: Called "cubed" (e.g., 5³ = 125).
Scientific Notation
Scientific notation is a way to express very large or very small numbers using exponents. It is written as a × 10^n, where 1 ≤ a < 10.
Examples:
3,000,000 = 3 × 10^6
0.00045 = 4.5 × 10^(-4)
Speed of light = 299,792,458 m/s ≈ 3 × 10^8 m/s
3,000,000 = 3 × 10^6
0.00045 = 4.5 × 10^(-4)
Speed of light = 299,792,458 m/s ≈ 3 × 10^8 m/s
Real-World Applications
- Compound Interest: A = P(1 + r)^t
- Population Growth: P(t) = P₀ × e^(rt)
- Computer Science: Memory sizes (2^10 = 1024 bytes = 1 KB)
- Physics: Newton's law of gravitation (inverse square law)
References
- Khan Academy. "Exponents and Powers." 2026.
- Purplemath. "Exponent Rules." 2026.