Fifth power (algebra)

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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:

1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ... (sequence A000584 in OEIS)

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.

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