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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:
Exponentiation is written as b n, where b is the base and n is the power; often said as "b to the power n ". [1] When n is a positive integer , exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [ 1 ] b n = b × b × ⋯ × b × b ⏟ n times . {\displaystyle b^{n}=\underbrace ...
In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n 6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube. The sequence of sixth ...
In arithmetic and algebra, the seventh power of a number n is the result of multiplying seven instances of n together. So: n 7 = n × n × n × n × n × n × n.. Seventh powers are also formed by multiplying a number by its sixth power, the square of a number by its fifth power, or the cube of a number by its fourth power.
Divisor function d(n) up to n = 250 Prime-power factors In number theory , a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors . Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
Thus, 1/54, in sexagesimal, is 1/60 + 6/60 2 + 40/60 3, also denoted 1:6:40 as Babylonian notational conventions did not specify the power of the starting digit. Conversely 1/4000 = 54/60 3 , so division by 1:6:40 = 4000 can be accomplished by instead multiplying by 54 and shifting three sexagesimal places.
The most basic R5 series consists of these five rounded numbers, which are powers of the fifth root of 10, rounded to two digits. The Renard numbers are not always rounded to the closest three-digit number to the theoretical geometric sequence: R5: 1.00 1.60 2.50 4.00 6.30
The only Pell numbers that are squares, cubes, or any higher power of an integer are 0, 1, and 169 = 13 2. [7] However, despite having so few squares or other powers, Pell numbers have a close connection to square triangular numbers. [8] Specifically, these numbers arise from the following identity of Pell numbers: