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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, exponentiation is an operation involving two numbers: the base and the exponent or power.
Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers.
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
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 ...
Associative property. In mathematics, the associative property[1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
Pentation is the next hyperoperation (infinite sequence of arithmetic operations) after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity). This is similar to as tetration is iterated right-associative exponentiation. [1] It is a binary operation defined with two numbers a and b, where a ...
Exponentiation is easily misconstrued: note that the operation of raising to a power is right-associative (see below). Tetration is iterated exponentiation (call this right-associative operation ^), starting from the top right side of the expression with an instance a^a (call this value c). Exponentiating the next leftward a (call this the ...
Fifth power (algebra) 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: