The first in the list of arithmetic actions there are an addition, subtraction, multiplication and also division. As independent operation the idea of exponentiation in the mathematical environment developed far not at once.
Number degree: what is it?
Definition of degree of number a having a natural indicator of n is defined for real number a. This number is called the degree basis. And natural number n carries the name of an exponent. The degree having a natural indicator is defined by the work: multiplication operation is the cornerstone of a concept of degree.
So, degree of number a having a natural indicator of n is the expression having an appearance: a^n. Its value equals to work n of multipliers, and each of them is equal to a.
By means of degree, works of several multipliers of an identical look can be written down. Example: work 6*6*6*6*6 can be written down as 6^5.
There are rules of reading degrees. Example: 7^6 it is read as "seven in degree six" or "seven in the sixth degree". In a general view the mathematical expression of a type of a^n is read thus: "an in n degree", "n-aya number a degree", "an in n-oh degree".
Some degrees have the long ago taken roots names. So, the second degree of any number is called its square, and the third degree – a cube of such number. Example: 2^3 are two cubed, and 4^2 – four in a square.
Number degree: from the history of emergence of a concept
It is considered to be that in degree the number began to be built to Entre Rios and Ancient Egypt. The first degrees of natural numbers were described in "Arithmetics" by Diophantus Aleksandriysky. Already in the Middle Ages the German scientists made an attempt to enter uniform designation for number degree. The significant role in it was played by the "Full arithmetics" made by Michel Stifel.
The French scientist Nikola Shyuke living about the 1500th year began to write an exponent more in small print on the right above from the degree basis. The same idea was used in the book "Algebra" by Italian Bombelli. Modern designation of degrees meets at René Descartes, the author of "Geometry".
Features of exponentiation
If to build unit in any natural degree, the same unit will turn out.
Any number if to build it in zero degree, will equal to unit.
Negative degree of any number can be transformed to positive: a^(-n) equals 1/a^n. In other words, the number having a negative indicator equals fractions. Unit will be its numerator, and this number taken with a positive indicator will act as a denominator.
How to multiply degrees which have the equal reasons? For this purpose the basis to leave to the same, and to summarize indicators is required.
In modern mathematics it is considered to be that expressions of a look 0^0 and 0^ (-n) do not make sense. Thus, to say about what zero is equal in negative degree, simply senselessly to.