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A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent . Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times. [ 1][ 2] The first ten powers of 2 for non-negative values of n are:
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".
In arithmetic and algebra, the fifth power or sursolid[ 1] of a number n is the result of multiplying five instances of n together: n5 = 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:
n. th root. In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root.
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...
In mathematics, high superscripts are used for exponentiation to indicate that one number or variable is raised to the power of another number or variable. Thus y 4 is y raised to the fourth power, 2 x is 2 raised to the power of x , and the equation E = mc 2 includes a term for the speed of light squared .
Tetration is also defined recursively as. allowing for attempts to extend tetration to non-natural numbers such as real, complex, and ordinal numbers . The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions.
Knuth's up-arrow notation. In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1] In his 1947 paper, [ 2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation ...
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