Exponent Calculator
An exponent is a mathematical notation that indicates how many times a base number is multiplied by itself. This calculator computes b^n (base raised to exponent) for any real base and exponent, including negative and fractional exponents. For example, 2^3 = 8 (2 multiplied by itself 3 times), while 2^(-2) = 0.25 (the reciprocal of 2 squared), and 8^(1/3) = 2 (the cube root of 8). The calculator automatically shows the logarithm inverse, allowing you to verify: if b^n = result, then log_b(result) = n. A reference table displays common powers of 2 (from 2^1 to 2^20) and powers of 10 (from 10^1 to 10^15), useful for quick reference and understanding exponential growth. Exponents are fundamental in algebra, calculus, physics, and finance, appearing in compound interest, scientific notation, and exponential functions.
Exponent formula
b^n = b × b × ... × b (n times)
b^(-n) = 1 / (b^n)
b^(m/n) = nth root of (b^m)
b^0 = 1 (for b ≠ 0)
Powers of 2 and 10
| Power of 2 | Result | Power of 10 | Result |
|---|---|---|---|
| 2^1 | 2 | 10^1 | 10 |
| 2^2 | 4 | 10^2 | 100 |
| 2^3 | 8 | 10^3 | 1,000 |
| 2^4 | 16 | 10^4 | 10,000 |
| 2^5 | 32 | 10^5 | 100,000 |
| 2^6 | 64 | 10^6 | 1,000,000 |
| 2^7 | 128 | 10^7 | 10,000,000 |
| 2^8 | 256 | 10^8 | 100,000,000 |
| 2^9 | 512 | 10^9 | 1,000,000,000 |
| 2^10 | 1,024 | 10^10 | 10,000,000,000 |
| 2^15 | 32,768 | 10^12 | 1,000,000,000,000 |
| 2^20 | 1,048,576 | 10^15 | 1,000,000,000,000,000 |
Exponent calculator: frequently asked questions
What is an exponent?
An exponent is a number that indicates how many times the base is multiplied by itself. For example, 2^3 means 2 × 2 × 2 = 8. The base is 2, and the exponent is 3. Exponents are also called powers.
What does a negative exponent mean?
A negative exponent means to take the reciprocal of the base raised to the positive exponent. For example, 2^(-3) = 1/(2^3) = 1/8 = 0.125. In general, a^(-n) = 1/(a^n).
What does a fractional exponent mean?
A fractional exponent represents a root. For example, 8^(1/3) is the cube root of 8, which equals 2 because 2 × 2 × 2 = 8. In general, a^(1/n) is the nth root of a, and a^(m/n) is the nth root of a raised to the mth power.
What is 0^0?
The value of 0^0 is undefined in mathematics. Different contexts treat it differently. In combinatorics, it is often defined as 1. This calculator treats 0^0 as undefined to reflect the mathematical convention.
How do logarithms relate to exponents?
Logarithms are the inverse of exponents. If b^n = x, then log_b(x) = n. For example, 2^3 = 8, so log_2(8) = 3. Logarithms are useful for solving equations where the exponent is unknown.
Official sources
- Exponents and powers: NIST Special Publication 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.