Fifth power (algebra)

In arithmetic and algebra, the fifth power of a number "n" is the result of multiplying five instances of "n" together:
Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube.
The sequence of fifth powers of integers is:
Properties.
The last digit of the fifth power of any real number x, with 10 as the base, is the last digit of x (irrational or floating point numbers are included).
By the Abel–Ruffini theorem, there is no general algebraic formula (formula expressed in terms of radical expressions) for the solution of polynomial equations containing a fifth power of the unknown as their highest power. This is the lowest power for which this is true. See quintic equation, sextic equation, and septic equation.
Along with the fourth power, the fifth power is one of two powers "k" that can be expressed as the sum of "k" − 1 other "k"-th powers, providing counterexamples to Euler's sum of powers conjecture. Specifically, 