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## 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 x^{n} . 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:

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