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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. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that
Yao's method collects in u first those x i that appear to the highest power ; in the next round those with power are collected in u as well etc. The variable y is multiplied h − 1 {\displaystyle h-1} times with the initial u , h − 2 {\displaystyle h-2} times with the next highest powers, and so on.
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.
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 .
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 .
In mathematics, an n th 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.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares.
A double exponential function is a constant raised to the power of an exponential function. The general formula is () = = (where a>1 and b>1), which grows much more quickly than an exponential function. For example, if a = b = 10: f(x) = 10 10 x; f(0) = 10; f(1) = 10 10; f(2) = 10 100 = googol; f(3) = 10 1000