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Eighth power
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Eighth power
In arithmetic and algebra, the eighth power of a number n is the result of multiplying eight instances of n together. So:
Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself.
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".
Polynomial equations of degree 8 are octic equations. These have the form
The smallest known eighth power that can be written as a sum of eight eighth powers is
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:
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Eighth power
In arithmetic and algebra, the eighth power of a number n is the result of multiplying eight instances of n together. So:
Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself.
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".
Polynomial equations of degree 8 are octic equations. These have the form
The smallest known eighth power that can be written as a sum of eight eighth powers is
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: