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For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. 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
Cube (algebra) y = x3 for values of 1 ≤ x ≤ 25. 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 23 = 8 or (x + 1)3. The cube is also the number ...
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
Power of 10. Visualisation of powers of 10 from one to 1 trillion. A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten ...
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has where e is the base of the natural logarithm, i is the imaginary unit, and ...
Applying the f function k times to the number n = 2 k a + b will give the result 3 c a + d, where d is the result of applying the f function k times to b, and c is how many increases were encountered during that sequence.
The term superexponentiation was published by Bromer in his paper Superexponentiation in 1987. [3] It was used earlier by Ed Nelson in his book Predicative Arithmetic, Princeton University Press, 1986. The term hyperpower [4] is a natural combination of hyper and power, which aptly describes tetration.