Fifth power (algebra)

In arithmetic and algebra, the fifth power of a number n is the result of multiplying five instances of n together. So:

n⁵ = n × n × n × n × n.

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:

0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, 161051, 248832, 371293, 537824, 759375, 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625, ... (sequence A000584 in the OEIS)

The last digit of the fifth power of a number n is the last digit of n.

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. See quintic equation, sextic equation, and septic equation.