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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 or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n.
The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 11 solar masses) due to Hawking radiation is on the order of 10 100 years. [7] Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future. A googol is considerably smaller than a centillion. [8]
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”.
Similarly, the expression b 3 = b · b · b is called "the cube of b" or "b cubed", because the volume of a cube with side-length b is b 3. When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
A Taxicab number is the smallest positive number that can be expressed as a sum of two positive integer cubes in n distinct ways. The smallest taxicab number after Ta(1) = 1, is Ta(2) = 1729, [4] expressed as
Analogously, the inverses of tetration are often called the super-root, and the super-logarithm (In fact, all hyperoperations greater than or equal to 3 have analogous inverses); e.g., in the function =, the two inverses are the cube super-root of y and the super-logarithm base y of x.
Here is an angle in the unit circle; taking 1 / 3 of that angle corresponds to taking a cube root of a complex number; adding −k 2 π / 3 for k = 1, 2 finds the other cube roots; and multiplying the cosines of these resulting angles by corrects for scale.