Exponentiation – widespread action in mathematics. Difficulties arise at emergence of zero degree. Not all numbers can be built in this degree, and for the others several general rules work.
Construction of numbers in zero degree
Construction in zero degree in algebra meets very often though definition of degree 0 demands additional explanations. Definition of zero degree includes the solution of this simplest example. Any equation is equal in zero degree to unit. It does not depend on that an integer or fractional, negative or positive. In this case there is only one exception: number zero for which other rules work. That is, what number you do not build in zero degree, only unit as a result will turn out. Any number of figures from 1 indefinitely, whole, fractional, positive and negative, rational and irrational at construction in zero degree turns into unit. Only the zero becomes an exception for this rule.
Construction of zero in degree
In mathematics it is not accepted builds zero in zero degree. The fact is that such example is impossible. Construction of zero in zero does not make sense. In this degree it is possible to build any number, except the zero.
In some examples cases when it is necessary to deal with zero degrees meet. It happens at simplification of expression to degrees. In that case zero degree can be replaced with unit and to further solve an example, without being beyond rules of mathematical exercises.
All becomes complicated a little if as a result of simplification the variable or expression with variables in zero degree appears. In that case there is an additional condition – the basis of degree needs to be made other than zero and after that to continue to solve the equation. An exact square of any number including zero, cannot terminate in figures 2, 3, 7 and 8 and also the odd number of zero. The second property of any square of natural number – it or is divided into 4, or at division on 8 gives the rest 1. There is also a property for division into 9 and on 3. The square of any natural number or is divided into nine, or at division into three gives the rest 1. The main properties of an exact square of natural numbers are that. It is possible to make sure of them by means of simple proofs and also by means of real examples.
Construction of zero in a square – a difficult task which is not studied at school. Zero increased by zero yield the same result therefore the example in itself is senseless and seldom meets in classical mathematics.