How to Use
- Enter the base
Input the base number for the exponentiation.
- Enter the exponent
Input the exponent value. Negative numbers and decimals are supported.
- View result
Click Calculate to see the result of the power calculation instantly.
What is an exponent (power)?
An exponent, or power, is the operation of multiplying the same number by itself several times. It is written as aⁿ, where the base a on the bottom is multiplied by itself n times (the exponent). For example, 2³ = 2 × 2 × 2 = 8, read as 'two to the power of three'.
Why use exponents?
- Compact notation for large numbers: 1,000,000 can be written more concisely as 10⁶.
- Compound growth: compound interest, population growth, and cell division that grow by a fixed rate each period are modeled in the form (1+r)ⁿ.
- Area and volume: a cube with a side of 5 has a volume of 5³ = 125.
This calculator handles not only integers but also negative exponents (reciprocals) and fractional or decimal exponents (roots) all at once, instantly computing large powers that are tedious to work out by hand.
Formula
The basic formula for a power is as follows.
result = base^exponent = aⁿ
- a (base): the number to multiply repeatedly
- n (exponent): the number of times to multiply
Example 1 — integer exponent: 3⁴ = 3 × 3 × 3 × 3 = 81
Example 2 — negative exponent: 2⁻³ = 1 / 2³ = 1 / 8 = 0.125
Example 3 — fractional exponent: 8^(1/3) = ³√8 = 2 (cube root)
This calculator rounds the result to up to 10 decimal places, and if the result grows too large to represent, it is shown as ∞.