Calculate any power instantly — enter a base and exponent to get the result and a full step-by-step solution.
What Is an Exponent?
An exponent (also called a power or index) tells you how many times to multiply a number by itself.
In the expression b^n:
- b is the base — the number being multiplied
- n is the exponent — how many times to multiply it
Example: 2^4 = 2 × 2 × 2 × 2 = 16
Exponent Rules
| Expression | Result | Rule |
|---|
| x^1 | x | Any number to the power of 1 equals itself |
| x^0 | 1 | Any non-zero number to the power of 0 equals 1 |
| x^(−n) | 1 / x^n | Negative exponent equals the reciprocal |
| x^0.5 | √x | Exponent 0.5 equals the square root |
| 0^n | 0 | Zero to any positive power equals zero |
| 1^n | 1 | One to any power equals one |
Worked Examples
Positive integer exponent:
3^4 = 3 × 3 × 3 × 3 = 81
Negative exponent:
2^(−3) = 1 / 2^3 = 1 / 8 = 0.125
Decimal exponent (square root):
9^0.5 = √9 = 3
Large exponent:
10^6 = 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000
Sources
Frequently Asked Questions
What is an exponent?
An exponent (also called a power or index) tells you how many times to multiply a base number by itself. In the expression 2^3, the base is 2 and the exponent is 3, so the calculation is 2 × 2 × 2 = 8.
What does a negative exponent mean?
A negative exponent means taking the reciprocal of the positive power. For example, 2^(−3) = 1 / 2^3 = 1/8 = 0.125. More generally, x^(−n) = 1 / x^n.
What is x^0?
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1, and (−7)^0 = 1. The expression 0^0 is mathematically debated — most calculators define it as 1 by convention.
What does a decimal exponent mean?
A decimal exponent represents a root. The exponent 0.5 is the square root — for example, 9^0.5 = √9 = 3. In general, x^(1/n) is the nth root of x.
Can the base be negative?
Yes, as long as the exponent is an integer. For example, (−2)^3 = (−2) × (−2) × (−2) = −8. A negative base with a decimal exponent (such as (−4)^0.5) produces a complex number, which this calculator does not support.