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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:
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
The first three values of the expression x[5]2. The value of 3[5]2 is 7 625 597 484 987; values for higher x, such as 4[5]2, which is about 2.361 × 10 8.072 × 10 153 are much too large to appear on the graph. In mathematics, pentation (or hyper-5) is the fifth hyperoperation.
In the third expression, n is the height, but each of the bases is different. Care must be taken when referring to iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated powers or iterated exponentials .
Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3 2, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x ^2 ( caret ) or x **2 may be used in place of x 2 .
If n is a power of an odd prime number the formula for the totient says its totient can be a power of two only if n is a first power and n − 1 is a power of 2. The primes that are one more than a power of 2 are called Fermat primes , and only five are known: 3, 5, 17, 257, and 65537.
By definition, in quarter-comma meantone 1 so-called "perfect" fifth (P5 in the table) has a size of approximately 696.6 cents ( 700 − ε cents, where ε ≈ 3.422 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 + 11 ε cents, which is about 737.6 ...
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3.