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In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = 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:
The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".
may mean that A is a subset of B, and is possibly equal to B; that is, every element of A belongs to B; expressed as a formula, ,. 2. A ⊂ B {\displaystyle A\subset B} may mean that A is a proper subset of B , that is the two sets are different, and every element of A belongs to B ; expressed as a formula, A ≠ B ∧ ∀ x , x ∈ A ⇒ x ∈ ...
n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n “tesseracted”, “hypercubed”, “zenzizenzic”, “biquadrate” or “supercubed” instead of “to the power of 4”.
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
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Kirchhoff's diffraction formula; Klein–Gordon equation; Korteweg–de Vries equation; Landau–Lifshitz–Gilbert equation; Lane–Emden equation; Langevin equation; Levy–Mises equations; Lindblad equation; Lorentz equation; Maxwell's equations; Maxwell's relations; Newton's laws of motion; Navier–Stokes equations; Reynolds-averaged ...
These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these. This article lists equations from Newtonian mechanics , see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics ).