In arithmetic and algebra, the eighth power of a number n is the result of multiplying eight instances of n together.
The sequence of eighth powers of integers is: In the archaic notation of Robert Recorde, the eighth power of a number was called the "zenzizenzizenzic".
These have the form The smallest known eighth power that can be written as a sum of eight eighth powers is[2] The sum of the reciprocals of the nonzero eighth powers is the Riemann zeta function evaluated at 8, which can be expressed in terms of the eighth power of pi: This is an example of a more general expression for evaluating the Riemann zeta function at positive even integers, in terms of the Bernoulli numbers: In aeroacoustics, Lighthill's eighth power law states that the power of the sound created by a turbulent motion, far from the turbulence, is proportional to the eighth power of the characteristic turbulent velocity.
[3][4] The ordered phase of the two-dimensional Ising model exhibits an inverse eighth power dependence of the order parameter upon the reduced temperature.
[5] The Casimir–Polder force between two molecules decays as the inverse eighth power of the distance between them.