Exponent Calculator — Calculate Powers (x^n)
Calculate the power of any number. Supports decimal bases, negative exponents, and shows results in both standard and scientific notation. See also Square Root Calculator and Log Calculator.
How to Calculate Exponents
An exponent tells you how many times to multiply a number (the base) by itself. For example, 2^3 means 2 × 2 × 2 = 8. Enter any base and exponent — including decimals and negative numbers — and the calculator will compute the result instantly. Negative exponents produce reciprocals: 2^(-3) = 1/(2^3) = 1/8 = 0.125. Fractional exponents represent roots: 8^(1/3) = ∛8 = 2.
Exponent Formula
x^n = x × x × x × ... (n times)
x^0 = 1 (for any x ≠ 0)
x^(-n) = 1 / x^n
x^(1/n) = ⁿ√x (nth root)
x^(a+b) = x^a × x^b
(x^a)^b = x^(a×b)
Example
2^10 = ?
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 4 × 4 × 4 × 4 × 4 (grouping pairs)
= 1,024
Frequently Asked Questions
What is any number raised to the power of 0?
Any non-zero number raised to the power of 0 equals 1. This is a mathematical convention that keeps the exponent rules consistent: x^n / x^n = x^(n-n) = x^0 = 1.
What happens with negative exponents?
A negative exponent means "take the reciprocal." So x^(-n) = 1/x^n. For example, 5^(-2) = 1/25 = 0.04.
Can I use decimal exponents?
Yes. A decimal exponent like 2^2.5 is equivalent to 2^(5/2) = 2^2 × 2^(1/2) = 4 × √2 ≈ 5.657. Fractional exponents represent roots combined with powers.
Why does a negative base with a fractional exponent give an error?
In real numbers, a negative base raised to a fractional power (like (-4)^0.5) involves taking an even root of a negative number, which is undefined. The result would be a complex number.