Jump to
Table of Contents
Share this
See also
Evaluate n-th root
Evaluate powers of 2
Evaluate lognx
Evaluate exponential
Evaluate ln(x)
All evaluation tools

N-th power calculator

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool evaluates the n-th power of a number: \(x^n\). Enter the the power degree n and the argument x below. Non integer n is supported.

n =
x =
Result:
\(x^n\) =
shape details
Table of Contents
Share this

Definitions

General

The n-th power of a number x, when n is an integer, is the result of multiplying x to itself n times (x*x*x...*x). In modern notation n-th root is written as xn . Typically degree n is an integer. For fractional powers, the result can be decomposed to an integer power and a radical. For example:

\[ x^{n/m} = \left(x^n\right)^{1/m} = \sqrt[m]{x^n} \]

For n=2 the power is called square while for n=3 cube. For n=0 the result is always 1, while for n=1 the power result renders the same x number.

Properties

The derivative of the principal n-th power function is:

\[ \left(x^n\right)' = n x^{n-1} \]

The integral of the n-th power function is given by:

\[ \int x^n\, \mathrm{d}x = \frac{1}{n+1} x^{n+1} +C \]

See also
Evaluate n-th root
Evaluate powers of 2
Evaluate lognx
Evaluate exponential
Evaluate ln(x)
All evaluation tools