Exponent Calculator
Base raised to a power
About This Calculator
An exponent indicates how many times a base number is multiplied by itself. Exponents are used in scientific notation, compound interest, computer science (powers of 2), and many areas of mathematics. Special rules apply for zero exponents, negative exponents, and fractional exponents.
Formula
b^n = b × b × ... × b (n times)
b^0 = 1 (any non-zero base)
b^(−n) = 1 / b^n
b^(1/n) = n-th root of b
Example Calculation
Calculate 2^10 and 5^3.
- 2^10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024
- 5^3 = 5 × 5 × 5 = 125
2^10 = 1,024; 5^3 = 125
Powers of 2
| Exponent | Value | Exponent | Value |
|---|---|---|---|
| 2^1 | 2 | 2^7 | 128 |
| 2^2 | 4 | 2^8 | 256 |
| 2^3 | 8 | 2^9 | 512 |
| 2^4 | 16 | 2^10 | 1,024 |
| 2^5 | 32 | 2^11 | 2,048 |
| 2^6 | 64 | 2^12 | 4,096 |
Frequently Asked Questions
What does a negative exponent mean?
A negative exponent means the reciprocal of the positive power. For example, 2^(−3) = 1/(2^3) = 1/8 = 0.125.
What is any number raised to the power of 0?
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1. Zero raised to the power of 0 is mathematically indeterminate.
What is a fractional exponent?
A fractional exponent represents a root. b^(1/2) = sqrt(b), b^(1/3) = cube root of b, and b^(m/n) = n-th root of b^m.